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Goro Akagi

Section

Graduate School of Science

Job title

Professor

Degree

博士（理学）（早稲田大学）
修士（理学）（早稲田大学）

researchmap

https://researchmap.jp/7000019121

J-GLOBAL ID

201701020786114863

Profile

研究業績一覧（日本語）http://www.math.tohoku.ac.jp/~akagi/achievement.html

Research History 10

2022/01 - Present

Shizuoka University　Faculty of Science　Specially Appointed Professor
2016/04 - Present

Tohoku University　Graduate School of Science Department of Mathematics　Full Professor
2021/09 - 2022/08

University of Pavia　Department of Mathematics　Contract Professor
2017/10 - 2018/03

Technical University of Munich　Department of Mathematics　Carl Friedrich von Siemens Research Fellowship of the Alexander von Humboldt Foundation
2015/09 - 2016/09

Technical University of Munich　Department of Mathematics　Carl Friedrich von Siemens Research Fellow of the Alexander von Humboldt Foundation
2011/04 - 2016/03

Kobe University　Graduate School of System Informatics Department of System Science　Associate Professor
2010/04 - 2011/03

Shibaura Institute of Technology　Department of Machinery and Control Systems, College of Systems Engineering and Science　Associate Professor
2006/04 - 2010/03

Shibaura Institute of Technology　Department of Machinery and Control Systems, College of Systems Engineering,　Lecture
2005/04 - 2006/03

Nihon University　College of Humanities and Sciences　PD Researcher
2003 - 2004

Waseda University　Media Network Center　Research Associate

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Education 3

Waseda University　Graduate School of Science and Engineering　Department of Physics and Applied Physics

2000/04 - 2004/09
Waseda University　Graduate School of Science and Engineering　Department of Physics and Applied Physics

1998/04 - 2000/03
Waseda University　School of Science and Engineering　Department of Physics

1994/04 - 2000/03

Professional Memberships 2

日本応用数理学会

2022/08 - Present
Mathematical Society of Japan

Research Interests 3

関数解析
発展方程式
応用解析学、発展方程式、関数解析

Research Areas 2

Natural sciences / Mathematical analysis / Evolution Equation, Functional Analysis
Natural sciences / Basic analysis / Evolution Equation, Functional Analysis

Awards 2

第６回福原賞

2014/12　函数方程式分科会（日本数学会）
Carl Friedrich von Siemens Research Fellowship of the Alexander von Humboldt Foundation

2014/11　Alexander von Humboldt Foundation

Papers 62

Weighted energy-dissipation approach to semilinear gradient flows with state-dependent dissipation

Goro Akagi, Ulisse Stefanelli, Riccardo Voso

Journal of Differential Equations　2025/09

DOI： 10.1016/j.jde.2025.113431 　
Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing

Goro Akagi, Hiroki Miyakawa

Journal of Elliptic and Parabolic Equations　2025/06/12

DOI： 10.1007/s41808-025-00339-2 　
Lyapunov stability of non-isolated equilibria for strongly irreversible Allen–Cahn equations

Goro Akagi, Messoud Efendiev

Proceedings of the Royal Society of Edinburgh: Section A Mathematics　2024/12/18

DOI： 10.1017/prm.2024.97 　
Generalized gradient flows for time-dependent energies and applications to PDEs involving variable exponents Peer-reviewed

Goro Akagi, Naoki Tanaka

Nonlinear Differential Equations and Applications　31　(5)　2024/09

DOI： 10.1007/s00030-024-00955-2 　

ISSN： 1021-9722

eISSN： 1420-9004
On a class of doubly nonlinear evolution equations in Musielak–Orlicz spaces Peer-reviewed

Goro Akagi, Giulio Schimperna

Mathematische Nachrichten　2024/07

DOI： 10.1002/mana.202300374 　
Fractional Dissipative PDEs Invited Peer-reviewed

Franz Achleitner, Goro Akagi, Christian Kuehn, Jens Markus Melenk, Jens D. M. Rademacher, Cinzia Soresina, Jichen Yang

Nonlinear Systems and Complexity　53-122　2024/04/16
Publisher: Springer Nature Switzerland
DOI： 10.1007/978-3-031-54978-6_3 　

ISSN： 2195-9994

eISSN： 2196-0003
Steady States with Jump Discontinuity in a Receptor-Based Model with Hysteresis in Higher-Dimensional Domains. Peer-reviewed

Goro Akagi, Izumi Takagi, Conghui Zhang

SIAM J. Math. Anal.　56　(2)　1996-2033　2024

DOI： 10.1137/22m1509059 　
Evolution equations with complete irreversibility and energy conservation Peer-reviewed

Goro Akagi, Kotaro Sato

Journal of Mathematical Analysis and Applications　2023/11

DOI： 10.1016/j.jmaa.2023.127348 　
Space-time homogenization for nonlinear diffusion Peer-reviewed

Goro Akagi, Tomoyuki Oka

Journal of Differential Equations　358　386-456　2023/06
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2023.01.044 　

ISSN： 0022-0396
General framework to construct local-energy solutions of nonlinear diffusion equations for growing initial data Peer-reviewed

Goro Akagi, Kazuhiro Ishige, Ryuichi Sato

Journal of Functional Analysis　284　(10)　109891-109891　2023/05
Publisher: Elsevier BV
DOI： 10.1016/j.jfa.2023.109891 　

ISSN： 0022-1236
Rates of Convergence to Non-degenerate Asymptotic Profiles for Fast Diffusion via Energy Methods Peer-reviewed

Goro Akagi

Archive for Rational Mechanics and Analysis　2023/04

DOI： 10.1007/s00205-023-01843-2 　
On some doubly-nonlinear parabolic equations posed in $ \mathbb{R}^{ { d } } $ Invited Peer-reviewed

Goro Akagi

Discrete and Continuous Dynamical Systems - S　16　(12)　3661-3676　2023
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI： 10.3934/dcdss.2023153 　

ISSN： 1937-1632

eISSN： 1937-1179
Local well-posedness for Frémond’s model of complete damage in elastic solids Peer-reviewed

GORO AKAGI, GIULIO SCHIMPERNA

European Journal of Applied Mathematics　33　(2)　309-327　2022/04
Publisher: Cambridge University Press ({CUP})
DOI： 10.1017/S0956792521000024 　

ISSN： 0956-7925

eISSN： 1469-4425

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We consider a model for the evolution of damage in elastic materials originally proposed by Michel Frémond. For the corresponding PDE system, we prove existence and uniqueness of a local in time strong solution. The main novelty of our result stands in the fact that, differently from previous contributions, we assume no occurrence of any type of regularising terms.
Traveling wave dynamics for Allen-Cahn equations with strong irreversibility Peer-reviewed

Goro Akagi, Christian Kuehn, Ken-Ichi Nakamura

Transactions of the American Mathematical Society　2022/02/04
Publisher: American Mathematical Society (AMS)
DOI： 10.1090/tran/8583 　

ISSN： 0002-9947

eISSN： 1088-6850

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Constrained gradient flows are studied in fracture mechanics to describe strongly irreversible (or unidirectional) evolution of cracks. The present paper is devoted to a study on the long-time behavior of non-compact orbits of such constrained gradient flows. More precisely, traveling wave dynamics for a one-dimensional fully nonlinear Allen-Cahn type equation involving the positive-part function is considered. Main results of the paper consist of a construction of a one-parameter family of degenerate traveling wave solutions (even identified when coinciding up to translation) and exponential stability of such traveling wave solutions with some basin of attraction, although they are unstable in a usual sense.
Correction to: Weighted Energy-Dissipation approach to doubly nonlinear problems on the half line Peer-reviewed

Goro Akagi, Stefano Melchionna, Ulisse Stefanelli

Journal of Evolution Equations　21　(4)　5203-5207　2021/12
Publisher: Springer Science and Business Media {LLC}
DOI： 10.1007/s00028-021-00698-y 　

ISSN： 1424-3199

eISSN： 1424-3202
Fractional flows driven by subdifferentials in Hilbert spaces Peer-reviewed

Akagi, G.

Israel Journal of Mathematics　234　(2)　809-862　2019/10

DOI： 10.1007/s11856-019-1936-9 　
Allen-Cahn equation with strong irreversibility Peer-reviewed

Akagi, G., Efendiev, M.

European Journal of Applied Mathematics　30　(4)　707-755　2019/08

DOI： 10.1017/S0956792518000384 　
Convergence of solutions for the fractional Cahn–Hilliard system Peer-reviewed

Goro Akagi, Giulio Schimperna, Antonio Segatti

Journal of Functional Analysis　276　(9)　2663-2715　2019/05

DOI： 10.1016/j.jfa.2019.01.006 　
Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint Peer-reviewed

Akagi, G., Melchionna, S.

Nonlinear Differential Equations and Applications　26　(2)　2019/04

DOI： 10.1007/s00030-019-0551-0 　
Unidirectional evolution equations of diffusion type Peer-reviewed

Akagi, G., Kimura, M.

Journal of Differential Equations　266　(1)　1-41　2019/01

DOI： 10.1016/j.jde.2018.05.022 　
Quantitative estimates on localized finite differences for the fractional poisson problem, and applications to regularity and spectral stability Peer-reviewed

Akagi, G., Schimperna, G., Segatti, A., Spinolo, L.V.

Communications in Mathematical Sciences　16　(4)　913-961　2018/10

DOI： 10.4310/CMS.2018.V16.N4.A2 　
Weighted Energy-Dissipation approach to doubly nonlinear problems on the half line Peer-reviewed

Goro Akagi, Stefano Melchionna, Ulisse Stefanelli

Journal of Evolution Equations　18　(1)　49-74　2018/03/01
Publisher: Birkhauser Verlag AG
DOI： 10.1007/s00028-017-0390-6 　

ISSN： 1424-3199
The Cauchy problem for the Finsler heat equation Peer-reviewed

Akagi, G., Ishige, K., Sato, R.

Advances in Calculus of Variations　13　(3)　257-278　2018
Publisher: Walter de Gruyter GmbH
DOI： 10.1515/acv-2017-0048 　

ISSN： 1864-8258

eISSN： 1864-8266
Elliptic-regularization of nonpotential perturbations of doubly-nonlinear flows of nonconvex energies: A variational approach Peer-reviewed

Akagi, G., Melchionna, S.

Journal of Convex Analysis　25　(3)　861-898　2018
Allen-Cahn equation with strong irreversibility

Goro Akagi, Messoud Efendiev

RIMS Kokyuroku, Analysis on Shapes of Solutions to Partial Differential Equations　2046　69-88　2017/10
Nondecreasing solutions to doubly nonlinear equations Peer-reviewed

Goro Akagi, Ulisse Stefanelli

Springer INdAM Series　22　31-53　2017
Publisher: Springer International Publishing
DOI： 10.1007/978-3-319-64489-9_2 　

ISSN： 2281-5198 2281-518X
Fractional Cahn-Hilliard, Allen-Calm and porous medium equations Peer-reviewed

Goro Akagi, Giulio Schimperna, Antonio Segatti

JOURNAL OF DIFFERENTIAL EQUATIONS　261　(6)　2935-2985　2016/09

DOI： 10.1016/j.jde.2016.05.016 　

ISSN： 0022-0396

eISSN： 1090-2732
Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion Peer-reviewed

Goro Akagi

COMMUNICATIONS IN MATHEMATICAL PHYSICS　345　(1)　77-100　2016/07

DOI： 10.1007/s00220-016-2649-0 　

ISSN： 0010-3616

eISSN： 1432-0916
A Variational Principle for Gradient Flows of Nonconvex Energies Peer-reviewed

Goro Akagi, Ulisse Stefanelli

JOURNAL OF CONVEX ANALYSIS　23　(1)　53-75　2016

ISSN： 0944-6532
Stability of stationary solutions for semilinear heat equations with concave nonlinearity Peer-reviewed

Goro Akagi, Ryuji Kajikiya

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS　17　(6)　2015/12

DOI： 10.1142/S0219199715500017 　

ISSN： 0219-1997

eISSN： 1793-6683
Stability analysis of asymptotic profiles for fast diffusion equations Peer-reviewed

Goro Akagi, Ryuji Kajikiya

NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS　64　183-191　2015
Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli Peer-reviewed

Goro Akagi, Ryuji Kajikiya

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE　31　(6)　1155-1173　2014/11

DOI： 10.1016/j.anihpc.2013.08.006 　

ISSN： 0294-1449
LOCAL SOLVABILITY OF A FULLY NONLINEAR PARABOLIC EQUATION Peer-reviewed

Goro Akagi

KODAI MATHEMATICAL JOURNAL　37　(3)　702-727　2014/10

DOI： 10.2996/kmj/1414674617 　

ISSN： 0386-5991
Sub differential calculus and doubly nonlinear evolution equations in L-P-spaces with variable exponents Peer-reviewed

Goro Akagi, Giulio Schimperna

JOURNAL OF FUNCTIONAL ANALYSIS　267　(1)　173-213　2014/07

DOI： 10.1016/j.jfa.2014.04.015 　

ISSN： 0022-1236

eISSN： 1096-0783
DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING VARIABLE EXPONENTS Peer-reviewed

Goro Akagi

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S　7　(1)　1-16　2014/02

DOI： 10.3934/dcdss.2014.7.1 　

ISSN： 1937-1632

eISSN： 1937-1179
DOUBLY NONLINEAR EQUATIONS AS CONVEX MINIMIZATION Peer-reviewed

Goro Akagi, Ulisse Stefanelli

SIAM JOURNAL ON MATHEMATICAL ANALYSIS　46　(3)　1922-1945　2014

DOI： 10.1137/13091909X 　

ISSN： 0036-1410

eISSN： 1095-7154
A minimization approach to gradient flows of nonconvex energies Peer-reviewed

AKAGI GORO

``Nonlinear Analysis and Interdisciplinary Sciences'', GAKUTO International Series, Mathematical Sciences and Applications　36　1-16　2013/11
Publisher: Gakko-tosho

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This note is concerned with a minimization approach to gradient ﬂows in Hilbert spaces H driven by nonconvex energies which can be decomposed into a sum of a convex part and a smooth part. More precisely, we introduce a Weighted EnergyDissipation (WED for short) functional W_\epsilon, which consists of a dissipation part and an energy part along with an exponential weight in ti
Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations Peer-reviewed

Goro Akagi, Ryuji Kajikiya

MANUSCRIPTA MATHEMATICA　141　(3-4)　559-587　2013/07

DOI： 10.1007/s00229-012-0583-9 　

ISSN： 0025-2611

eISSN： 1432-1785
Stability and instability of asymptotic profiles of solutions for fast diffusion equations Invited

AKAGI GORO

RIMS Kokyuroku　1845　1-12　2013/06
Publisher: RIMS

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In this note, we review the authors’ recent results on the stability analysis of asymptotic proﬁles of solutions to the CauchyDirichlet problem for the fast diﬀusion equation.
Stability and instability of group invariant asymptotic profiles for fast diffusion equations Peer-reviewed

Goro Akagi

Springer INdAM Series　2　1-16　2013
Publisher: Springer International Publishing
DOI： 10.1007/978-88-470-2841-8_1 　

ISSN： 2281-5198 2281-518X
Nonlinear diffusion equations driven by the p(·)-Laplacian Peer-reviewed

Goro Akagi, Kei Matsuura

Nonlinear Differential Equations and Applications　20　(1)　37-64　2013
Publisher: Springer
DOI： 10.1007/s00030-012-0153-6 　

ISSN： 1021-9722 1420-9004
Periodic solutions for doubly nonlinear evolution equations Peer-reviewed

Goro Akagi, Ulisse Stefanelli

JOURNAL OF DIFFERENTIAL EQUATIONS　251　(7)　1790-1812　2011/10

DOI： 10.1016/j.jde.2011.04.014 　

ISSN： 0022-0396
WELL-POSEDNESS AND LARGE-TIME BEHAVIORS OF SOLUTIONS FOR A PARABOLIC EQUATION INVOLVING p(x)-LAPLACIAN Peer-reviewed

Goro Akagi, Kei Matsuura

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS　31　22-31　2011/09

ISSN： 1078-0947

eISSN： 1553-5231
Weighted energy-dissipation functionals for doubly nonlinear evolution Peer-reviewed

Goro Akagi, Ulisse Stefanelli

JOURNAL OF FUNCTIONAL ANALYSIS　260　(9)　2541-2578　2011/05

DOI： 10.1016/j.jfa.2010.12.027 　

ISSN： 0022-1236
Maximal monotonicity for the sum of two subdifferential operators in L-p-spaces Peer-reviewed

Goro Akagi

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS　74　(5)　1664-1671　2011/03

DOI： 10.1016/j.na.2010.10.037 　

ISSN： 0362-546X
Doubly nonlinear evolution equations with non-monotone perturbations in reflexive Banach spaces Peer-reviewed

Goro Akagi

JOURNAL OF EVOLUTION EQUATIONS　11　(1)　1-41　2011/03

DOI： 10.1007/s00028-010-0079-6 　

ISSN： 1424-3199
Global attractors for doubly nonlinear evolution equations with non-monotone perturbations Peer-reviewed

Goro Akagi

JOURNAL OF DIFFERENTIAL EQUATIONS　250　(4)　1850-1875　2011/02

DOI： 10.1016/j.jde.2010.10.019 　

ISSN： 0022-0396
A variational principle for doubly nonlinear evolution Peer-reviewed

Goro Akagi, Ulisse Stefanelli

APPLIED MATHEMATICS LETTERS　23　(9)　1120-1124　2010/09

DOI： 10.1016/j.aml.2010.04.047 　

ISSN： 0893-9659
Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian Peer-reviewed

Goro Akagi, Petri Juutinen, Ryuji Kajikiya

MATHEMATISCHE ANNALEN　343　(4)　921-953　2009/04

DOI： 10.1007/s00208-008-0297-1 　

ISSN： 0025-5831
Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian Peer-reviewed

Goro Akagi, Kazumasa Suzuki

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS　31　(4)　457-471　2008/04

DOI： 10.1007/s00526-007-0117-6 　

ISSN： 0944-2669
Local existence of solutions to some degenerate parabolic equation associated with the p-Laplacian Peer-reviewed

Goro Akagi

JOURNAL OF DIFFERENTIAL EQUATIONS　241　(2)　359-385　2007/10

DOI： 10.1016/j.jde.2007.05.009 　

ISSN： 0022-0396
WBT content for geography and geology using VRML

Akagi, G., Anada, K., Miyadera, Y., Shimizu, M., Tsuchida, K., Yaku, T., Yasui, M.

IFIP International Federation for Information Processing　230　2007
Publisher: IFIP International Federation for Information Processing
DOI： 10.1007/978-0-387-69312-5_11 　
On a certain degenerate parabolic equation associated with the infinity-Laplacian

Akagi, G., Suzuki, K.

Discrete and Continuous Dynamical Systems- Series A　(SUPPL.)　2007
Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces Peer-reviewed

Goro Akagi

JOURNAL OF DIFFERENTIAL EQUATIONS　231　(1)　32-56　2006/12

DOI： 10.1016/j.jde.2006.04.006 　

ISSN： 0022-0396
On some macroscopic models for type-II superconductivity Peer-reviewed

G. Akagi, M. Otani

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS　63　(5-7)　E1155-E1166　2005/11

DOI： 10.1016/j.na.2005.03.037 　

ISSN： 0362-546X
Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces Peer-reviewed

G Akagi, M Otani

JOURNAL OF DIFFERENTIAL EQUATIONS　209　(2)　392-415　2005/02

DOI： 10.1016/j.jde.2004.08.011 　

ISSN： 0022-0396
Convergence of functionals and its applications to parabolic equations Peer-reviewed

Goro Akagi

Abstract and Applied Analysis　2004　(11)　907-933　2004/12/15
Publisher: Hidawi Publisher
DOI： 10.1155/S1085337504403030 　

ISSN： 1085-3375
Asymptotic behavior of solutions for parabolic equations associated with $p$-Laplacian as $p$ tends to infinity Peer-reviewed

AKAGI GORO

GAKUTO International Series, Mathematical Sciences and Applications　20　pp.418-429　2004
Publisher: Gakkotosho
Time-dependent constraint problems arising from macroscopic critical-state models for type-II superconductivity and their approximations Peer-reviewed

Goro Akagi, Mitsuharu Otani

Advances in Mathematical Sciences and Applications　14　(2)　pp.683-712　2004
Publisher: Gakkotosho
ISSN： 1343-4373
Evolution inclusions governed by subdifferentials in reflexive Banach spaces Peer-reviewed

G Akagi, M Otani

JOURNAL OF EVOLUTION EQUATIONS　4　(4)　519-541　2004

DOI： 10.1007/s00028-004-0162-y 　

ISSN： 1424-3199
PRINCIPLE OF SYMMETRIC CRITICALITY AND EVOLUTION EQUATIONS Peer-reviewed

Goro Akagi, Jun Kobayashi, Mitsuharu Otani

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS　1-10　2003

ISSN： 1078-0947

eISSN： 1553-5231
EVOLUTION EQUATIONS AND SUBDIFFERENTIALS IN BANACH SPACES Peer-reviewed

Goro Akagi, Mitsuharu Otani

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS　supplement volume　11-20　2003

ISSN： 1078-0947

eISSN： 1553-5231

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Misc. 6

A subdifferential approach to evolution equations in variable exponent Lebesgue spaces (New Role of the Theory of Abstract Evolution Equations : From a Point of View Overlooking the Individual Partial Differential Equations)

Akagi Goro

RIMS Kokyuroku　1892　73-87　2014/04
Publisher: Kyoto University
ISSN： 1880-2818
A global variational principle for nonlinear evolution (Analysis on non-equilibria and nonlinear phenomena : from the evolution equations point of view)

Akagi Goro

RIMS Kokyuroku　1792　40-56　2012/05
Publisher: Kyoto University
ISSN： 1880-2818
A random walk model for nonlinear diffusion (Viscosity Solutions of Differential Equations and Related Topics)

Akagi Goro

RIMS Kokyuroku　1695　12-27　2010/07
Publisher: Kyoto University
ISSN： 1880-2818
非線形拡散方程式の解の漸近形の解析

赤木剛朗

特別教育・研究報告集　378-381　2010
Publisher: 芝浦工業大学連携推進部
ISSN： 2185-7326
Doubly nonlinear evolution equations and dynamical systems (Nonlinear Evolution Equations and Mathematical Modeling)

Akagi Goro

RIMS Kokyuroku　1640　56-66　2009/04
Publisher: Kyoto University
ISSN： 1880-2818
Doubly nonlinear evolution equation and its applications (Evolution Equations and Asymptotic Analysis of Solutions)

Akagi Goro, Otani Mitsuharu

RIMS Kokyuroku　1358　117-137　2004/02
Publisher: Kyoto University
ISSN： 1880-2818

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Presentations 139

Research Achievements

Goro Akagi

2023/04/01
Rate of convergence to asymptotic profiles for fast diffusion equations Invited

2022/09/06
Evolution equations with irreversibility constraints Invited

Goro Akagi

Inverse Problems and Control for PDEs and the Hamilton-Jacobi Equation: French-Italian-Japanese conference　2022/06/14
Gradient flow theory for time-dependent energies and applications to nonlinear PDEs

2022/03/31
Local well-posedness for some phase-field model of complete damage Invited

Russia-Japan Workshop, Mathematical analysis of, fracture phenomena for elastic structures, its applications, t Conference of Continuum Mechanics Focusing on Singularities, CoMFo

Goro Akagi　2021/12/15
Rates of convergence to asymptotic profiles for fast diffusion Invited

2021/12/10
Rates of convergence to asymptotic profiles for fast diffusion Invited

2021/11/06
Energy method for quantitative analysis of rates of convergence to asymptotic profiles for fast diffusion Invited

Goro Akagi

PDE Seminars, The Hong Kong University of Science and Technology　2021/10/15
Rates of convergence to non-degenerate asymptotic profiles for fast diffusion via energy methods Invited

2021/10/06
Traveling wave dynamics for a one-dimensional constrained Allen-Cahn equation Invited

Goro Akagi

Asia-Pacific Analysis and PDE Seminar, The University of Sydney　2021/09/13
Rates of convergence to non-degenerate asymptotic profiles for fast diffusion equations via an energy method Invited

Goro Akagi

BIRS-CMO Workshop ``New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry'', Banff International Research Station for Mathematical Innovation and Discovery (BIRS) and Casa Matemática Oaxaca　2021/09/08
非線形拡散方程式の解の漸近挙動について－発展方程式の立場から－ Invited

赤木剛朗

第 42 回発展方程式若手セミナー　2021/08/30
Traveling wave dynamics for constrained Allen-Cahn equations Invited

Goro Akagi

The 46 th Sapporo;Symposium on Partial Differential Equations　2021/08/12
A framework for proving existence of local-energy solutions to doubly-nonlinear diffusion equations with growing initial data Invited

2021/04/08
Traveling wave dynamics for Allen-Cahn equations with strongly irreversibile constraints Invited

Goro Akagi

Nancy-Tohoku premeeting　2021/01/26
Exponential stability of traveling waves for a constrained Allen-Cahn equation Invited

Goro Akagi

Qualitative properties for nonlinear;diffusion equations　2020/01/22
Traveling wave dynamics for Allen-Cahn equations with non-decreasing constraints Invited

Goro Akagi

Chemotaxis and Nonlinear Parabolic Equations　2019/11/06
Fractional gradient flows in Hilbert spaces Invited

2019/10/26
単調成長を拘束条件に持つ勾配系について Invited

赤木剛朗

Musashino Center of Mathematical Engineering Seminar 28, 武蔵野大学　2019/10/24
Traveling wave dynamics for the Allen-Cahn equation with non-decreasing constraint Invited

Goro Akagi

Mathematicsl Aspects of Surface and Interface Dynamics 18　2019/10/17
Traveling wave dynamics for the Allen-Cahn equation with non-decreasing constraint Invited

Goro Akagi

Kanazawa workshop: Gradient flows and related topics: analysis and applications　2019/08/09
Traveling wave dynamics for the Allen-Cahn equation with the positive-part function Invited

Goro Akagi

2019/07/19
Traveling wave dynamics for the Allen-Cahn equation with non-decreasing constraint Invited

Goro Akagi

Oberseminar Analysis, Fakultät für Mathematik, Technische Universität Dresden　2019/07/02
Traveling wave dynamics for the Allen-Cahn equation with strong irreversibility Invited

信州大学偏微分方程式研究集会　2019/06/29
Traveling wave dynamics for the Allen-Cahn equation with non-decreasing constraint Invited

2019/06/21
Fractional Cahn-Hilliard system and Łojasiewicz-Simon gradient inequality Invited

2019/04/12
Fractional gradient flows in Hilbert spaces Invited

Goro Akagi

AMS Spring Central and Western Joint Sectional Meeting　2019/03/23
Partial energy-dissipation and smoothing effect for constrained Allen-Cahn equations Invited

Goro Akagi

BIRS Workshop "Phase-Field Models of Fracture"　2019/03/05
Fast Diffusion Equation and asymptotic profiles of solutions Invited

2019/02/15
Fast Diffusion 方程式とその解の漸近形について Invited

赤木剛朗

大岡山談話会　2018/12/17
Asymptotic behavior of solutions to an Allen-Cahn type equation with a non-decreasing constraint Invited

Goro Akagi

International Workshop on Nonlinear PDEs 2018 in Okayama　2018/12/14
Allen-Cahn equation with non-decreasing constraint in unbounded domains Invited

2018/11/05
拘束条件付き Allen-Cahn 方程式に由来する自由境界値問題について

赤木剛朗

研究集会「芝浦工大における微分方程式セミナー」　2018/08/24
Convergence of solutions for fractional Cahn-Hilliard systems

Goro Akagi

The 10th International Conference on Dynamical Systems and Differential Equations　2018/07/07
Partial energy-dissipation and smoothing effect for constrained Allen-Cahn equations

Goro Akagi

The 10th International Conference on Dynamical Systems and Differential Equations　2018/07/06
Stability analysis of asymptotic profiles for fast diffusion Invited

Goro Akagi

Workshop on Nonlinear Parabolic PDEs　2018/06/12
Convergence of solutions for fractional Cahn-Hilliard systems Invited

Goro Akagi

8th Euro-Japanese Workshop on Blow-Up　2018/06/05
Allen-Cahn equation with a non-decreasing constraint Invited

Goro Akagi

Workshop ``UK-Japan Workshop on Analysis of Nonlinear Partial Differential Equations''　2018/05/18
Fractional flows driven by subdifferentials International-presentation Invited

Goro Akagi

Seminario di Matematica Applicata, IMATI-CNR e Dipartimento di Matematica, Università degli studi di Pavia　2018/03/06
Fractional flows driven by subdifferentials International-presentation Invited

Goro Akagi

Dipartimento di Matematica, Università degli studi di Trento　2018/02/27
Evolution equations with nondecreasing constraint International-presentation Invited

Goro Akagi

Workshop ``Trends in variational evolution''　2018/02/21
Evolution equations with nondecreasing constraint International-presentation

Goro Akagi

Seminar der Lehlstuhl M6, Zentrum Mathematik, Technische Universität München　2018/02/08
Evolution equations arising from non-standard irreversible models International-presentation Invited

Goro Akagi

Dresdner Mathematisches Seminar, Fakultät für Mathematik, Technische Universität Dresden　2017/12/20
Stability analysis of asymptotic profiles for fast diffusion International-presentation Invited

Goro Akagi

Oberseminar Analysis, Fakultät für Mathematik, Technische Universität Dresden　2017/12/14
Fractional variant of the Brézis-Kōmura theory and perspectives Invited

AKAGI Goro

2017/10/26
Partial smoothing effect and energy-dissipation for an Allen-Cahn equation with non-decreasing constraint Invited

AKAGI Goro

2017/09/30
Partial smoothing and energy-dissipation of a constrained Allen-Cahn equation Invited

AKAGI Goro

2017/09/01
Gradient inequality and application to stability analysis of asymptotic profiles for fast diffusion Invited

AKAGI Goro

2017/08/03
Allen-Cahn equation with non-decreasing constraint, Invited

AKAGI Goro

2017/07/07
Stability analysis of asymptotic profiles for fast diffusion Invited

AKAGI Goro

2017/06/30
勾配不等式とその応用について Invited

赤木剛朗

岩手数理科学セミナー　2017/06/06
An application of gradient inequalities to stability analysis for asymptotic profiles of fast diffusion International-presentation

Goro Akagi

International Conference on Elliptic and Parabolic Problems　2017/05/23
Strongly irreversible gradient flows International-presentation Invited

OIST Mini Symposium: Viscoelasticity and Dissipative Dynamics of Rods and Membranes, OIST (Okinawa Institute of Science and Technology　2017/03/08
Fast diffusion 方程式の漸近形と gradient inequality

第六回北海道-東北コンソーシアムセミナー, コラッセふくしま　2017/02/13
Asymptotic profiles of solutions to fast diffusion equations and their stability Invited

松山解析セミナー2017　2017/02/04
Strongly irreversible Allen-Cahn equation Invited

九州函数方程式セミナー, 福岡大学セミナーハウス　2016/11/25
Allen-Cahn equation with strong irreversibility Invited

研究集会「偏微分方程式の解の形状解析」, 京都大学数理解析研究所　2016/11/10
Stability of asymptotic profiles for fast diffusion Invited

談話会, 東北大学大学院理学研究科数学専攻　2016/11/07
Stability analysis of accumulating profiles for fast diffusion Invited

2016/10/21
On some fully nonlinear Allen-Cahn type equation Invited

応用数学セミナー, 東北大学大学院理学研究科数学専攻　2016/10/20
Fractional Cahn-Hilliard equations Invited

研究集会「発展方程式論とその非線形解析への応用」, 京都大学数理解析研究所　2016/10/13
Stability and instability of asymptotic profiles for fast diffusion International-presentation Invited

``7th Euro-Japanese Workshop on Blow-up'', The Mathematical Research and Conference Center　2016/09/08
Allen-Cahn type equation with strong irreversibility International-presentation Invited

University of Trento　2016/07/26
Recent developments in doubly nonlinear evolution equations International-presentation Invited

The 5th International conference ``Nonlinear Analysis and Extremal Problems'', Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences (SB RAS)　2016/06/20
Allen-Cahn type equation with strong irreversibility International-presentation Invited

``Entropy methods, dissipative systems, and applications'' during Themantic Program ``Nonlinear Flows'', Erwin Schrödinger International Institute for Mathematics and Physics (ESI)　2016/06/17
Stability analysis of non-isolated asymptotic profiles for fast diffusion International-presentation Invited

Seminar on Partial Differential Equations, Institute of Mathematics of the Czech Academy of Sciences　2016/05/17
Gradient flows with strong irreversibility International-presentation Invited

Seminario di Matematica Applicata, IMATI-CNR e Dipartimento di Matematica, University of Pavia　2016/05/10
Stability and instability of asymptotic profiles for the fast diffusion equation International-presentation Invited

Weierstrass Institute for Applied Analysis and Stochastics　2016/05/04
Stability and instability of asymptotic profiles for fast diffusion International-presentation Invited

Oberseminar Analysis / Joint Analysis Seminar Augsburg-München　2016/04/14
Non-standard irreversible processes and nonlinear evolution equations International-presentation Invited

ICB Seminar, Helmholtz Zentrum Muenchen　2016/02/29
Fast Diffusion 方程式の消滅解の漸近形に対する安定性解析 -- 孤立していない漸近形の安定性について -- Invited

2015/07/08
Stability of non-isolated asymptotic profiles of least energy for FDE Invited

研究集会「第 2 回大阪駅前セミナー」　2015/07/03
Local solvability of a fully nonlinear parabolic equation with strong irreversibility International-presentation Invited

Special Materials in Complex Systems -- SMaCS 2015 INdAM Workshop　2015/05/18
Stability of non-isolated asymptotic profiles for fast diffusion

AKAGI Goro

日本数学会 2014 年度年会　2015/03
Stability of non-isolated asymptotic profiles of least energy for fast diffusion Invited

AKAGI Goro

研究集会「第 7 回福島応用数学研究集会」　2015/03
発展方程式と変分原理 Invited

AKAGI Goro

神戸スタジオセミナー　2015/02
Stability of non-isolated asymptotic profiles for fast diffusion Invited

AKAGI Goro

熊本大学応用解析セミナー　2015/02
Stability of non-isolated asymptotic profiles of least energy for fast diffusion Invited

AKAGI Goro

神戸解析セミナー　2015/01
分数冪ラプラシアンを含む Cahn-Hilliard 方程式について Invited

AKAGI Goro

研究集会「第 3 回現象の数理」　2015/01
Stability of non-isolated asymptotic profiles of least energy for the fast diffusion equation Invited

AKAGI Goro

第 185 回広島数理解析セミナー　2015/01
Local solvability of some fully nonlinear equation related to damage mechanics

AKAGI Goro

第 40 回発展方程式研究会　2014/12
Stability of non-isolated asymptotic profiles for the fast diffusion equation Invited

AKAGI Goro

第 594 回『応用解析』研究会　2014/12
Stability of non-isolated asymptotic profiles for fast diffusion Invited

AKAGI Goro

Nonlinear PDE Workshop at Tohoku University　2014/11
Stability analysis of non-isolated asymptotic profiles for fast diffusion Invited

AKAGI Goro

SNP 2014　2014/11
Doubly nonlinear evolution equations in variable exponent Lebesgue spaces

AKAGI Goro

日本数学会 2014 年度秋季総合分科会　2014/09
On a variational approach to stability analysis of asymptotic profiles for nonlinear diffusion International-presentation Invited

AKAGI Goro

Souel ICM 2014 Satellite Conference on Variational Methods for Nonlinear Elliptic PDEs　2014/08/04
Some fully nonlinear parabolic equation and unidirectional evolution International-presentation

AKAGI Goro

The 10th International Conference on Dynamical Systems and Differential Equations SS86　2014/07
Fast diffusion方程式の消滅解の漸近形状とその安定性解析 Invited

AKAGI Goro

神戸幾何学セミナー　2014/04
On some diffusion equation with strong irreversibility International-presentation Invited

Goro Akagi

Nonlinear Phenomena in Biology, Physics and Mechanics　2014/03/03

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強い不可逆性を有する拡散方程式の可解性、解の漸近挙動について発表した。
Fractional Cahn-Hilliard equations

AKAGI GORO

SAMS 21th Symmposium for Applied Analysis　2014/03

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Fractional Cahn-Hilliard equationに関する近年の研究成果を発表した。
Semilinear heat equation with concave nonlinearity Invited

AKAGI GORO

南大阪応用数学セミナー　2014/01

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sublinear heat equationの解の漸近挙動に関する近年の研究成果を報告した。
Symmetry and stability of asymptotic profiles for fast diffusion Invited

Goro Akagi

第31回九州における偏微分方程式研究集会　2014/01

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fast diffusion 方程式の漸近形の安定性解析に関する近年の研究成果を発表した。
Asymptotic profiles for fast diffusion

AKAGI GORO

第 2 回現象の数理　2014/01

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fast diffusion 方程式の漸近形の安定性解析に関する近年の研究成果を発表した。
非線形拡散方程式と解の漸近挙動 Invited

AKAGI GORO

卓越した大学院拠点形成支援事業平成25年度シンポジウム　2013/12

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fast diffusion 方程式の漸近形の安定性解析に関する近年の研究成果を発表した。
Nonlinear diffusion equation with strong irreversibility

AKAGI GORO

偏微分方程式研究集会　2013/11

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強い不可逆性を有する拡散方程式の可解性、解の漸近挙動について発表した。
Subdifferential calculus and evolution equations in variable exponent Lebesgue spaces Invited

Goro Akagi

RIMS研究集会「抽象的発展方程式の新たなる役割」　2013/10

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変動指数を含む二重非線形発展方程式に関する近年の研究成果を発表した。
非線形拡散方程式の解の漸近挙動 Invited

AKAGI GORO

日本数学会 2013 年度秋季総合分科会　2013/09/24

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fast diffusion 方程式の漸近形の安定性解析に関する近年の研究成果を発表した。
On some nonlinear parabolic equation involving variable exponents International-presentation Invited

Goro Akagi

Workshop ``DIMO-2013'' Diffuse Interface Models　2013/09/10

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変動指数を含む二重非線形発展方程式に関する近年の研究成果を発表した。
Diffusion equation with strong irreversibility International-presentation Invited

Goro Akagi

3rd Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's　2013/09/10

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強い不可逆性を有する拡散方程式の可解性、解の漸近挙動について発表した。
Subdifferential calculus and doubly nonlinear evolution equations involving variable exponents

AKAGI GORO

2013 秋の偏微分方程式セミナー　2013/09

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変動指数を含む二重非線形発展方程式に関する近年の研究成果を発表した。
Stability of asymptotic profiles for fast diffusion equations Invited

AKAGI GORO

京都駅前セミナー　2013/07

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fast diffusion 方程式の漸近形の安定性解析に関する近年の研究成果を発表した。
On an irreversible diffusion equation International-presentation Invited

Goro Akagi

Recent Advances in Partial Differential Equations and Applications　2013/06/17

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強い不可逆性を有する拡散方程式の可解性、解の漸近挙動について発表した。
非線形拡散方程式とその解の挙動について Invited

AKAGI GORO

HMMCセミナー　2013/05

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非線形拡散方程式の解の漸近挙動に関する近年の研究成果を発表した。
非線形拡散方程式の解の挙動について Invited

AKAGI GORO

研究集会「不均質媒質における異常拡散の数理と環境問題への応用」　2013/03

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非線形拡散方程式の解の漸近挙動に関するこれまでの研究をレビューした。
多孔質媒体中の流体拡散シミュレーション Invited

AKAGI GORO

学術研究発表会「新技術の研究」　2013/02

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多孔質媒体中の流体拡散シミュレーションに関してマクロモデル、ミクロモデルの双方の視点から２０１２年度の研究成果をレビューした。
Stability analysis of asymptotic profiles for fast diffusion

AKAGI GORO

Functional Analysis and Applications　2013/02

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
Stability analysis of asymptotic profiles for fast diffusion International-presentation Invited

AKAGI GORO

Seminario di Matematica Applicata　2013/01

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
Lojasiewicz-Simon 不等式と発展方程式の解の収束 Invited

AKAGI GORO

研究集会「非線型現象の数理モデルに現れる近平衡解の時間的漸近挙動に関する研究」　2013/01

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Lojasiewicz-Simon 不等式と発展方程式の解の収束に関する Feireisl-Simondon らの理論とその後の発展に関してレビューした。
Nonlinear evolution equations arising from parabolic PDEs with variable exponents

AKAGI GORO

第 38 回発展方程式研究会　2012/12

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変動指数が入った非線形放物型方程式の解の構成に関する結果を報告した。
Stability analysis of symmetric asymptotic profiles for fast diffusion equations and applications to semilinear elliptic equations Invited

AKAGI GORO

第3回「移流と拡散の数理」　2012/12

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
A minimization approach to gradient flows of non-convex energies International-presentation Invited

AKAGI GORO

5th Poliah-Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences -- Modellings, Theory and Simulations　2012/11/05

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非凸なエネルギー汎関数に対する勾配系に対する変分的定式化について近年得られた結果を報告した。
Review on an energy method for Lipschitz regularity estimates

AKAGI GORO

富山基礎解析セミナー　2012/10

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エネルギー評価を用いた非線形放物型方程式のリプシッツ評価の方法についてレビューを行った。
Doubly nonlinear parabolic equations involving variable exponents

AKAGI GORO

日本数学会 2012 年度秋季総合分科会, 実関数論分科会　2012/09

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変動指数が入った非線形放物型方程式の解の構成に関する結果を報告した。
Symmetry breaking of least energy solutions of Emden-Fowler equations

AKAGI GORO

日本数学会 2012 年度秋季総合分科会, 関数方程式論分科会　2012/09

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半線形楕円型方程式の最小エネルギー解の対称性の破れに関して最近得られた結果を報告した。
Symmetry and stability of asymptotic profiles for fast diffusion equations

AKAGI GORO

日本数学会 2012 年度秋季総合分科会, 関数方程式論分科会　2012/09

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
A global variational principle for gradien flows Invited

AKAGI GORO

東北大学非線形偏微分方程式ワークショップ　2012/09

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非凸なエネルギー汎関数に対する勾配系に対する変分的定式化について近年得られた結果を報告した。
A variational approach to gradient flows

AKAGI GORO

Partial Differential Equations in Osaka　2012/08

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非凸なエネルギー汎関数に対する勾配系に対する変分的定式化について近年得られた結果を報告した。
Stability analysis of asymptotic profiles for fast diffusion equations International-presentation

AKAGI GORO

SS01, The 9th International Conference on Dynamical Systems and Differential Equations and Applications　2012/07

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
Doubly nonlinear parabolic equations with variable exponents International-presentation

AKAGI GORO

SS15, The 9th International Conference on Dynamical Systems and Differential Equations and Applications　2012/07

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変動指数が入った非線形放物型方程式の解の構成に関する結果を報告した。
Asymptotic profiles for fast diffusion Invited

AKAGI GORO

九州関数方程式セミナー　2012/06

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
Symmetry and stability of asymptotic profiles for fast diffusion Invited

AKAGI GORO

なかもず解析セミナー　2012/04

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fast diffusion 方程式の解の漸近形の安定性の定義と分類法に関する近年の研究成果を報告した。
A global variational principle for non-equilibrium systems International-presentation Invited

Goro Akagi

CONFERENCE ON: Evolution Equations, Related Topics and Applications　2012/03/19
Mathematical analysis of nonlinear diffusion International-presentation Invited

Goro Akagi

ESF-JSPS Frontier Science Conference Series for Young Researchers "Mathematics for Innovation: Large and Complex Systems"　2012/03
Nonlinear diffusion equations associated with p(x)-Laplacians

赤木剛朗

第 100 回神楽坂解析セミナー　2012/01
Symmetry and stability of asymptotic profiles for fast diffusion

赤木剛朗

愛媛大学解析セミナー　2012/01
A variational principle for doubly nonlinear evolution problems

赤木剛朗

第 37 回発展方程式研究会　2011/12
Stability and instability of asymptotic profiles for fast diffusion International-presentation

Goro Akagi

MFO Workshop: Variational Methods for Evolution　2011/12
Nonlinear diffusion equations involving p(x)-Laplacians International-presentation Invited

Goro Akagi

Dutch-Japanese Workshop, Analysis of non-equilibrium evolution problems: selected topics in material and life sciences　2011/11/07
A global variational method for non-equilibrium systems

Goro Akagi

Workshop on the 3rd Service Mathematics　2011/11
A global variational principle for nonlinear evolution

Goro Akagi

RIMS研究集会「非平衡非線形現象の解析-発展方程式の立場から-」　2011/10
Stability analysis of asymptotic profiles of solutions for fast diffusion equations International-presentation Invited

Goro Akagi

The 4th MSJ-SI ``Nonlinear Dynamics in PDEs''　2011/09/12
Fast diffusion 方程式の解の漸近形の安定性解析 (空間 N 次元の場合)

赤木剛朗, 梶木屋龍治

日本数学会 2011 年度秋季総合分科会, 関数方程式論分科会　2011/09
二重非線型発展方程式の周期解

赤木剛朗, Ulisse Stefanelli

日本数学会 2011 年度秋季総合分科会, 実関数論分科会　2011/09
Symmetry and stability of asymptotic profiles of solutions for fast diffusion equations

赤木剛朗, 梶木屋龍治

研究集会「岐阜大学における微分方程式セミナー」　2011/09
Fast diffusion 方程式とある半線形楕円型方程式について

赤木剛朗

研究集会「サマーセミナー in 佐世保 2011」　2011/08
Nonlinear diffusion equations involving variable exponent

Goro Akagi

研究集会「Summer Seminar on PDE in 2011」　2011/08
Stability and instability of asymptotic profiles of solutions for fast diffusion equations International-presentation Invited

Goro Akagi

Second Italian-Japanese Workshop on Geometric Properties of Parabolic and Elliptic PDE's　2011/06/20
Stability of asymptotic profiles of solutions for the fast diffusion equation

赤木剛朗

第 147 回広島数理解析セミナー　2011/06
Fast diffusion 方程式の解の漸近形の安定性解析について

赤木剛朗

神戸大学解析セミナー　2011/05

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Research Projects 17

Evolution equations describing singularities of non-equilibrium systems beyond the linear-response regime and development of nonlocal-nonlinear analysis

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

Institution: Tohoku University

2024/04/01 - 2029/03/31
Quantitative analysis for nonlinear evolution equations of diffusion type

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))

Institution: Tohoku University

2021/10/07 - 2027/03/31
Mathematical analysis of inverse problems and modelling for complex fluids and diffusion in heterogeneous media

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)

Category: Grant-in-Aid for Scientific Research (A)

Institution: The University of Tokyo

2020/04/01 - 2025/03/31
Evolution equations with the coexistence of fractional derivatives and nonlinear structures -perturbation theory and asymptotic analysis-

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Research (Exploratory)

Institution: Tohoku University

2021/07/09 - 2024/03/31
Evolution equations describing non-standard irreversible processes --Analysis on singularities emerging in the dynamics of solutions--

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2020/04/01 - 2024/03/31
Analysis of singular nonlinear structure in dissipative systems

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)

Category: Grant-in-Aid for Scientific Research (A)

Institution: Tokyo Institute of Technology

2017/04/01 - 2022/03/31
Evolution equations with the coexistence of fractional derivatives and nonlinear structures

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Research (Exploratory)

Category: Grant-in-Aid for Challenging Research (Exploratory)

Institution: Tohoku University

2018/06/29 - 2021/03/31
Well-posedness for differential equations in metric spaces

Tanaka Naoki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Shizuoka University

2016/04/01 - 2020/03/31

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This research is based on the concept of the continuous dependence of solutions on initial data. The first purpose is to extend the study of the well-posedness for differential equations in Banach spaces to the study to express the dissipative structure of equations by metric-like functionals. The second purpose is to provide a new framework for well-posed theory that is beyond vector spaces, without compactness. The following topics were discussed: (1) Product formulas for semigroups of Lipschitz operators and its application to the approximate solvability of mixed problems of differential equations, (2) The general theory of evolution equations with fractional derivatives, (3) Mutational analysis by dissipativity in terms of a family of metrics, (4) Quasilinear theory without assuming that the domains of quasilinear operators are dense, (5) Product formulas for gradient flows in metric spaces and its application to gradient flows governed by perturbations of functionals.
Evolution equations describing non-standard irreversible processes Competitive

Akagi Goro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2016/04/01 - 2020/03/31

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Irreversible phenomena represented by diffusion are major factors of important phenomena closely related to our life such as unidirectionality of time, aging of lives and fracture. Classical theories for irreversible phenomena have already been established in the last century. However, many important irreversible phenomena beyond the scope of the classical theories have been observed, and therefore, studies of mathematical analysis have been developed in order to analyze and understand those new phenomena. In this research project, we have developed a new framework on Evolution Equations for covering new mathematical models which describe various non-standard irreversible phenomena. In particular, principal methods of analysis have been established for phase-field equations with strong irreversibility arising from fracture and damage models as well as nonlocal evolution equations involving fractional Laplacians, and moreover, systematic research has been done for those equations.
Study on nonlinear partial differential equations with set-valued perturbations

Otani Mitsuharu, AKAGI GOROU, ISHIWATA MICHINORI

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Waseda University

2015/04/01 - 2019/03/31

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We studied the existence of solutions of the initial value problem and the time periodic problem for the following semilinear parabolic equations: du/dt - △u + β(u) + G(x,t,u) = f(x,t) with the homogeneous Dirichlet boundary condition. Here β(u) is a (multi-valued) monotone operator and the perturbation term G(x,t,u) is a upper semi-continuous or lower semi-continuous set-valued function, which is a generalized notion of continuous function. When G is a set-valued function, there was no results even for super-linear cases. In our study, we succeeded in generalize the best result for the case where G is single-valued to the case where G is a set-valued function.
Nonlinear analysis for a parabolic-parabolic chemotaxis-growth system of equations

Osaki Koichi, Nakaguchi Etsushi, Tsujikawa Tohru, Kuto Kousuke, Akagi Goro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Kwansei Gakuin University

2014/04/01 - 2019/03/31

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We studied a parabolic-parabolic chemotaxis system with logistic growth. We showed the global-in-time existence of solutions to the chemotaxis system which has subquadratic degradation and nonlinear secretion. In addition, we showed the bifurcation of nontrivial solutions from the uniform state of the system, which indicates pattern formations, for instance, hexagonal and regular nesting patterns.
Research on Evolution Equations Describing Anomalous Diffusion Competitive

Akagi Goro, Shirakawa Ken, Ueda Yoshihiro, Ishiwata Tetsuya, Takeuchi Shingo

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Kobe University

2013/04 - 2016/03

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In natural and social phenomena, diffusion phenomena often play a crucial role. The classical theory on diffusion phenomena has already been established in the last century; however, there arose many diffusion phenomena presenting peculiar appearance beyond the scope of the classical theory. Such exceptional diffusion phenomena are classified as "anomalous diffusion" and attracting much interest in various fields. In this research project, a mathematical theory is developed in order to analyze anomalous diffusion. More precisely, the so-called "nonlinear diffusion" models, which are formulated in terms of nonlinear partial differential equations, are mainly treated. Furthermore, fundamental issues such as the well-posedness of each equation are justified and asymptotic behaviors and profiles of solutions are revealed. By virtue of solving each problem, we have developed a mathematical theory for anomalous diffusion.
Studies on approximate problems, regularity and singularity for mean curvature flow

ISHII Katsuyuki, NAITO Yuki, UEDA Yoshihiro, TAKAHASHI Futoshi, KUWAMURA Masataka, OHNUMA Masaki, AKAGI Goro, ISHIWATA Tetsuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Kobe University

2012/04/01 - 2015/03/31

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In this research project we study some approximate problems, regularity and singularity for the motion of a curve or a surface by its mean curvature, called mean curvature flow. We study some threshold-type algorithms for mean curvature flow, which is proposed by Chambolle in 2004. We prove the convergence of his algorithm by using the mathematical morphology in image processing, the level-set method, the signed distance function and the theory of viscosity solutions. As an application, we prove the convergence to the planar motion of a curve by non-smooth interface energies. As for the generalized mean curvature flow constructed by the above algorithms we show that if it does not fatten and the gradient of the auxiliary fucntion of the generalized flow does not vanish, then the generalized motion becomes smooth near such portions. We obtain some idea to prove the convergence of an algorithm for mean curvature flow in higher codimension and can expect the future study.
Asymptotic behavior of solutions for evolution equations involving nonlinear Laplacians

AKAGI Goro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

Category: Grant-in-Aid for Young Scientists (B)

2010 - 2012

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In various nonlinear problems, we often encounter nonlinear elliptic operators as modified forms of the classical (linear) Laplacian. In this research, we consider evolution equations governed by such nonlinear operators and investigate asymptotic behavior of solutions and their mechanism. More precisely, we revealed long-time behavior of solutions for diffusion-type equations involving p(x)-Laplacians with variable exponents and the infinity-Laplacian, and moreover, we also established a novel theory of stability analysis of asymptotic profiles for vanishing (in finite time) solutions of fast diffusion equations.
Synthetic study of nonlinear evolution equation and its related topics

OTANI Mitsuharu, YAMADA Yoshio, TANAKA Kazunaga, NISHIHARA Kenji, ISHII Hitoshi, OZAWA Tohru, OGAWA Takayoshi, KENMOCHI Nobuyuki, KOIKE Shigeaki, SAKAGUCHI Shigeru, SUZUKI Takashi, HAYASHI Nakao, IDOGAWA Tomoyuki, ISHIWATA Michinori, AKAGI Gorou

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

Category: Grant-in-Aid for Scientific Research (B)

Institution: Waseda University

2009 - 2012

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Various types of nonlinear PDEs (nonlinear elliptic equations, nonlinear diffusion equations, nonlinear wave equations, nonlinear Schrodinger equations) arising in physics and engineering were synthetically studied from the viewpoint of the theory of nonlinear evolution equations by using the techniques from the theory of nonlinear functional analysis, the theory of functions of a real variable, the theory of ordinary differential equations and the calculus of variations.
Research on evolution equations involving nonlinear Laplace operators

AKAGI Goro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

Category: Grant-in-Aid for Young Scientists (B)

Institution: Shibaura Institute of Technology

2007 - 2009

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Sufficient conditions for the existence of local (in time) solutions of some evolution equations involving p-Laplace operators are obtained. Moreover, the well-posedness of some evolution equation involving the infinity-Laplace operator is proved, and furthermore, the asymptotic behaviors (e.g., decay rates) of solutions are also revealed. Finally, a couple of effective methods are established in order to construct solutions and analyze their large-time behaviors for evolution equations involving nonlinear Laplace operators through this research project.
対称臨界性原理とその非線形偏微分方程式への応用

大谷光春, 北田韶彦, 田中和永, 松浦啓, 石渡通徳, 赤城剛朗, 小林純

Offer Organization: 日本学術振興会

System: 科学研究費助成事業萌芽研究

Category: 萌芽研究

Institution: 早稲田大学

2003 - 2005

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対称臨界性原理とは、「Banach空間X上で定義された汎関数Jに対し、ある群Gの作用に関して不変な部分空間X_G上でのJの臨界点が、X全体でのJの臨界点を与える」という原理である。この原理は、Jの汎関数(フレッシェ)微分を、劣微分作用素を含むかなり一般的な多価作用素Aに置き換えても成立することが、本研究により示されている。さらに、作用素Aが、必ずしも変分構造を有していない場合に対して拡張することが可能(AがG-共変であれば十分)であり、時間発展を伴う発展方程式に対して有用であろうことが期待されていた。 (1)非線形放物型方程式、波動方程式、シュレンディンガー方程式等への応用考えるとき、時間に関する微分作用素d/dtがどのような空間でG-共変となるかを調べることは重要であるが、今回L2(0,T;X),X=L2(Ω),L2(Ω)xL2(Ω),H10(Ω)xL2(Ω),などでそのG-共変性(G=O(N))が確かめられた。これらの空間は、上記の諸方程式を抽象発展方程式に帰着させるときに現れる基本的な空間であり、これは、今後の発展方程式への応用研究において重要な知見である。 (2)放物型方程式の時間大域解の漸近挙動を解析する際、コンパクト性は強力なな道具を提供する。一般の非有界領域では欠如しているソボレフの埋蔵定理にかかわるコンパクト性が、回転対称性を有する関数からなる部分空間においては、恢復するという事実に基づき、ある種の回転対称性を有する非有界領域におけp-Laplace作用素と爆発項を含む非線形放物型方程式の対称大域解のW1,p-有界性が確かめられた。

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Teaching Experience 41

Analysis B2 Exercise　Tohoku University
Analysis B2 (Measure Theory 2)　Tohoku University
Nonlinear Analysis (Variational Methods for Nonlinear Analysis)　Tohoku University
Analysis B1 (Measure Theory 1)　Tohoku University
Introdunctive Analysis C (Introduction to Fourier Analysis)　Tohoku University
Introdunction to PDEs　Tohoku University
Analysis A1 (Complex Analysis)　Tohoku University
Topology A　Tohoku University
Analysis B2 (Measure Theory 2)　Tohoku University
Analysis B1 (Measure Theory 1)　Tohoku University
Mathematical Statistic (Common Education)　Tohoku University
Advanced Functional Analysis　Tohoku University
Mathematical Statistic (Common Education)　Tohoku University
Nonlinear Analysis (Introduction to Nonlinear Semigroup Theory)　Tohoku University
Analysis D (Functional Analysis)　Tohoku University
Analysis C (Ordinary Differential Equations, Common Education)　Tohoku University
Analysis C (Differential Equations)　Tohoku University
Analysis C (Ordinary Differential Equations, Common Education)　Tohoku University
Introductive Analysis (Vector Analysis)　Tohoku University
Analysis C (Differential Equations)　Tohoku University
Analysis A2 (Complex Analysis 2)　Tohoku University
Analysis A1 Exercise　Tohoku University
Analysis A1 (Complex Analysis)　Tohoku University
Advanced Functional Analysis　Tohoku University
Vector Analysis　Kobe University
Ordinary Differential Equations　Kobe University
Numerical Analysis　Kobe University
Theory of System Innovation　Kobe University
Advanced Applied Mathematics　Kobe University
Introduction to Calculus　Kobe University
Discrete Mathematics　Kobe University
Fundamental Seminar on Mathematical Sciences　Shibaura Institute of Technology
Applied Mathematics　Shibaura Institute of Technology
Differential Equations　Shibaura Institute of Technology
Exercises in Mathematics 1　Shibaura Institute of Technology
Mathematics 1　Shibaura Institute of Technology
Exercises in Information Processing 2　Shibaura Institute of Technology
Information Processing 2　Shibaura Institute of Technology
Numerical Analysis　Shibaura Institute of Technology
Complex Analysis　Shibaura Institute of Technology
Network Technology I-IV　Waseda University

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Social Activities 3

宇都宮高校・出張講義

2018/11/09 - 2018/11/09
Sendai Math Seminar

2018/08 - 2018/08
Introduction to variational problems

2016/12/01 - 2016/12/01

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川井財団からの紹介で、仙台第一高等学校に於いて開催された「2016現代数学講演会」に講師として参加し、「変分問題入門 -最適性を問う数学-」という題目で講義を行った。

Other 3

発展方程式に対する新しい変分法の展開とその応用

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幾何光学、古典力学、熱力学、電磁気学、量子力学をはじめとする物理学の多くが変分原理によって定式化され、その理論的視点が多くの発展をもたらしていることは周知の事実である。それに伴い、汎関数の極値問題を解析するために様々な手法が開発され、変分法は物理学的にも数学的にも非常に強力な解析ツールとして知られている。一方、非平衡系の物理に現れる発展方程式（拡散方程式など）には勾配構造（ある汎関数を最小化する方向に状態が発展していく構造）があることが知られており、変分構造を持つ現象への過渡的過程を記述するものとして理解されている。従って、勾配系自体を変分原理に基づいて定式化し解析する視点はあまりない。本研究計画では、非平衡系の時間発展を記述する勾配構造を持った発展方程式に対する変分原理を模索し、汎関数の解析的・幾何学的な性質を解析することで発展方程式の解の定性的・定量的な性質を明らかにする新しい変分法の開発を目的とする。さらに発展方程式に対する変分的視点を応用することで、既に変分構造が知られ研究されている諸問題に対して新しい視点を与える。さらに、両国の参加研究者が本研究課題の枠を超えて共通の問題意識を模索し、今後長期間に渡って両国間の研究交流の要となり、より広範囲な研究交流のネットワークを構築していくための土台を作ること目標とする。また、本研究は非線形解析、数値解析、数理物理など複数の分野に関連するものである。その基本となるアイディアは単純であり、他分野への応用性が高い。そのため、本事業は我が国の非線形解析研究の継承と発展に加え、工学などへの波及効果を通して社会生活の向上に対する貢献が期待される。今回のプロジェクトでは、平成 24,25 年度に採択された二国間交流事業（イタリアとの共同研究）ではじまった本共同研究の成果を、ますます発展・展開させていく。
発展方程式に対する新しい変分法とその応用

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幾何光学、古典力学、熱力学、電磁気学、量子力学をはじめとする物理学の多くが変分原理によって定式化され、その理論的視点が多くの発展をもたらしていることは周知の事実である。それに伴い、汎関数の極値問題を解析するために様々な手法が開発され、変分法は物理学的にも数学的にも非常に強力な解析ツールとして知られている。一方、非平衡系の物理に現れる発展方程式（拡散方程式など）には勾配構造（ある汎関数を最小化する方向に状態が発展していく構造）があることが知られており、変分構造を持つ現象への過渡的過程を記述するものとして理解されている。従って、勾配系自体を変分原理に基づいて定式化し解析する視点はあまりない。本研究計画では、非平衡系の時間発展を記述する勾配構造を持った発展方程式に対する変分原理を模索し、汎関数の解析的・幾何学的な性質を解析することで発展方程式の解の定性的・定量的な性質を明らかにする新しい変分法の開発を目的とする。さらに発展方程式に対する変分的視点を応用することで、既に変分構造が知られ研究されている諸問題に対して新しい視点を与えることを目指す。さらに、両国の参加研究者が本研究課題の枠を超えて共通の問題意識を模索し、今後長期間に渡って両国間の研究交流の要となり、より広範囲な研究交流のネットワークを構築していくための土台を作ること目標とする。また、本研究は非線形解析、数値解析、数理物理など複数の分野に関連するものである。その基本となるアイディアは単純であり、他分野への応用性が高い。そのため、本事業は我が国の非線形解析研究の継承と発展に加え、工学などへの波及効果を通して社会生活の向上に対する貢献が期待される。
エネルギー消散を伴う非平衡系に適用可能な新しい変分法とその応用

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エネルギー消散を伴う非平衡系を記述する発展方程式に対する新しい変分原理を提案し、それに基づいた変分法の開発に取り組んだ。