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Evolution equations describing non-standard irreversible processes --Analysis on singularities emerging in the dynamics of solutions--

Research Project

Project/Area Number 20H01812
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionTohoku University

Principal Investigator

赤木 剛朗  東北大学, 理学研究科, 教授 (60360202)

Co-Investigator(Kenkyū-buntansha) 木村 正人  金沢大学, 数物科学系, 教授 (70263358)
梶木屋 龍治  大阪電気通信大学, 共通教育機構, 教授 (10183261)
上田 好寛  神戸大学, 海事科学研究科, 准教授 (50534856)
藤江 健太郎  東北大学, 理学研究科, 准教授 (50805398)
Project Period (FY) 2020-04-01 – 2024-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2023: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2022: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2021: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2020: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Keywords発展方程式 / 非線形拡散 / 不可逆過程 / 破壊・損傷力学モデル / 勾配流理論 / 非線形・非局所 / 距離空間上の勾配系の摂動理論
Outline of Research at the Start

拡散現象や相転移現象などの不可逆過程は, 時間の流れや老いなどの生命現象を理解する上で欠かせない. それらの古典論が前世紀末に確立されたが, 土壌汚染の拡散や物質の破損をはじめとする古典論の範疇を逸脱する様々な不可逆的現象が知られるようになり, またその特異な様相が現象の核心的特徴となることから, そのメカニズム解明が多くの注目を集めている. ここでは異常拡散や破壊現象をはじめとする古典論の枠組みから逸脱するような不可逆過程を記述する発展方程式を扱い, 方程式に内在する様々な構造を効率的に活用することのできる数学理論を構築し, 応用として解の漸近挙動に現れる特異性を定性的・定量的に分析する.

Outline of Annual Research Achievements

1. 破壊力学等に現れる強い不可逆性を有する散逸系の研究 当初予定されていた計画は既に完了している. ここでは研究期間中に派生した追加課題としてエネルギー保存則を満たす強い不可逆性を保つ発展方程式のクラスに着目し, その適切性や解の性質・漸近挙動について解析した. 特に強い不可逆性, 片側最小性, エネルギー保存則を同時に満たす発展方程式という観点で問題設定を行い, 包括的な研究を行ったのはこの研究課題の独自性と言える.
2. 非整数階微分作用素を含む発展方程式の研究 当初予定されていた計画は既に完了している. 追加課題として, 非整数階微分を伴う発展方程式の解の漸近挙動に関する研究を行い, 特に (非整数階微分版の) 勾配系の解がエネルギー汎関数の最小元に収束することを, あるクラスの凸汎関数に対して証明した. この結果はまだ展開が期待されるため, さらなる改良に取り組む.
3. 距離空間上の勾配流に対する摂動理論とその応用 -部分的勾配構造 距離空間上の勾配流には変分法が不可欠な役割を果たしてきた. 一方, 摂動問題は変分構造を壊してしまうため, 変分法の直接的な適用は期待できない. ここでは距離空間上の勾配流に対して導入した摂動理論の枠組みを用いることで, (単純化のためヒルベルト空間上の) 勾配系に対する摂動問題の可解性を直接的に変分法を用いることで証明している. この結果は U. Stefanelli 氏, R. Voso 氏 (ウィーン大) との共同研究で, 論文として投稿中である. 当初予定されていた課題は概ね完了した.
4. 非線形拡散方程式に対する解挙動の定量解析 定量的勾配不等式の開発がここでの最大の発見と言える. この不等式は解の収束レートを特定するような定量的情報を引き出すことができる. 結果は論文として出版された. 当初予定されていた課題は完了した.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

当初, 本研究計画で予定されていた課題は概ね解決している. またその過程で生じた追加課題についても成果が得られており, 順調に進展していると言える. 新たに浮上した課題も複数あり, ここまでに得られた結果をさらに発展させるための見通しも既に立っている. また研究成果も論文として取りまとめられており, 投稿中のものも複数ある. さらに国内外の研究集会などで研究成果を発表しており, 興味を持った関連分野の研究者から延長線上にある問題に関する問い合わせもあり, 今後のさらなる展開が期待される. また本研究計画の成果を踏まえ, 発展方程式論とその周辺分野に関するレクチュアノートを作成中であり, 今後, 大学院生や新規参入する研究者がいち早く理論の基礎を把握できるように研究資料として活用する. さらに発展方程式若手セミナーをはじめ, 発展方程式論とその周辺分野を専門とする若手研究者の活動を奨励し, 人材育成にも務めた. 一方, 関連分野の研究者の招聘やこちらからの訪問による研究成果の発表や情報交換に関しては, 先方の都合と合致せずに見合わせることになった. 今後, 予定が調整でき次第, 招聘・訪問を実施する.

Strategy for Future Research Activity

研究課題における問題解決は概ね完了しているので, 延長期間中は主に成果報告や論文発表に取り組む. 特に 2023 年度は海外が見送られた日本・イタリアの合同シンポジウムは 2024 年度中に開催が予定されているため, それを通して複数の国際的な研究グループが交流する場を設け, そこで当該研究課題で得られた成果についても議論したい. またレクチャーノートなどの整備は継続し, 本研究課題の成果を盛り込んだ資料の完成を目指す.

Report

(3 results)
  • 2022 Annual Research Report
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • Research Products

    (78 results)

All 2024 2023 2022 2021 2020 Other

All Int'l Joint Research (14 results) Journal Article (29 results) (of which Int'l Joint Research: 14 results,  Peer Reviewed: 28 results,  Open Access: 10 results) Presentation (26 results) (of which Int'l Joint Research: 12 results,  Invited: 19 results) Remarks (3 results) Funded Workshop (6 results)

  • [Int'l Joint Research] パヴィア大学(イタリア)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] ウィーン大学(オーストリア)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] ミュンヘン工科大学/ドレスデン工科大学(ドイツ)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] マドリード自治大学(スペイン)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] ウィーン大学(オーストリア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] パヴィア大学(イタリア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] ミュンヘン工科大学/ドレスデン工科大学(ドイツ)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Keimyung University(梶木屋 龍治)(韓国)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Chinese Academy of Sciences(藤江健太郎)(中国)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] ウィーン大学(オーストリア)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] パヴィア大学(イタリア)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] ミュンヘン工科大学/ドレスデン工科大学(ドイツ)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Keimyung University(梶木屋 龍治)(韓国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Chinese Academy of Sciences(藤江健太郎)(中国)

    • Related Report
      2020 Annual Research Report
  • [Journal Article] Steady States with Jump Discontinuity in a Receptor-Based Model with Hysteresis in Higher-Dimensional Domains2024

    • Author(s)
      Akagi Goro、Takagi Izumi、Zhang Conghui
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 56 Issue: 2 Pages: 1996-2033

    • DOI

      10.1137/22m1509059

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An energy estimate and a stabilized Lagrange-Galerkin scheme for a multiphase flow model2024

    • Author(s)
      Rudiawan Aufa, Zak Alexander, Benes Michal, Kimura Masato, Notsu Hirofumi
    • Journal Title

      Applied Mathematics Letters

      Volume: 153 Pages: 109059-109059

    • DOI

      10.1016/j.aml.2024.109059

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Universal approximation properties for an ODENet and a ResNet: Mathematical analysis and numerical experiments2024

    • Author(s)
      Aizawa Yuto, Kimura Masato, Matsui Kazunori
    • Journal Title

      Discrete and Continuous Dynamical Systems - B

      Volume: 29 Issue: 1 Pages: 351-376

    • DOI

      10.3934/dcdsb.2023099

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Memory Effects on the Stability of Viscoelastic Timoshenko Systems in the Whole 1<i>D</i>-Space2023

    • Author(s)
      Jorge Silva Marcio Antonio, Ueda Yoshihiro
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 66 Issue: 2 Pages: 71-123

    • DOI

      10.1619/fesi.66.71

    • ISSN
      0532-8721
    • Year and Date
      2023-08-15
    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Rates of Convergence to Non-degenerate Asymptotic Profiles for Fast Diffusion via Energy Methods2023

    • Author(s)
      Akagi Goro
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: 247 Issue: 2

    • DOI

      10.1007/s00205-023-01843-2

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] General framework to construct local-energy solutions of nonlinear diffusion equations for growing initial data2023

    • Author(s)
      Akagi Goro、Ishige Kazuhiro、Sato Ryuichi
    • Journal Title

      Journal of Functional Analysis

      Volume: 284 Issue: 10 Pages: 109891-109891

    • DOI

      10.1016/j.jfa.2023.109891

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Space-time homogenization for nonlinear diffusion2023

    • Author(s)
      Akagi Goro、Oka Tomoyuki
    • Journal Title

      Journal of Differential Equations

      Volume: 358 Pages: 386-456

    • DOI

      10.1016/j.jde.2023.01.044

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Evolution equations with complete irreversibility and energy conservation2023

    • Author(s)
      Akagi Goro、Sato Kotaro
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 527 Issue: 1 Pages: 127348-127348

    • DOI

      10.1016/j.jmaa.2023.127348

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On some doubly-nonlinear parabolic equations posed in R^d2023

    • Author(s)
      Akagi Goro
    • Journal Title

      Discrete and Continuous Dynamical Systems - S

      Volume: 16 Issue: 12 Pages: 3661-3676

    • DOI

      10.3934/dcdss.2023153

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation of nodal solutions for the Moore-Nehari differential equation.2023

    • Author(s)
      R. Kajikiya
    • Journal Title

      Nonlinear Differential Equations and Applications

      Volume: 30 Issue: 1

    • DOI

      10.1007/s00030-022-00816-w

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A short remark on comparison estimates in a chemotaxis system with local sensing2023

    • Author(s)
      Fujie Kentaro
    • Journal Title

      Discrete and Continuous Dynamical Systems - B

      Volume: - Issue: 10 Pages: 5355-5360

    • DOI

      10.3934/dcdsb.2023017

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property2023

    • Author(s)
      Islam Md. Sahidul, Kimura Masato, Miyata Hisanori
    • Journal Title

      Mathematics

      Volume: 11 Issue: 12 Pages: 2770-2770

    • DOI

      10.3390/math11122770

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Lack of the strict dissipativity and modification for the dissipative Bresse system2023

    • Author(s)
      Suzuki Tomoyuki, Ueda Yoshihiro
    • Journal Title

      Journal of Differential Equations

      Volume: 347 Pages: 24-55

    • DOI

      10.1016/j.jde.2022.11.030

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay for thermoelastic Green-Lindsay plates in bounded and unbounded domains2023

    • Author(s)
      Quintanilla Ramon, Racke Reinhard, Ueda Yoshihiro
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 22 Issue: 1 Pages: 167-191

    • DOI

      10.3934/cpaa.2022149

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Local well-posedness for Fr?mond’s model of complete damage in elastic solids2022

    • Author(s)
      AKAGI GORO、SCHIMPERNA GIULIO
    • Journal Title

      European Journal of Applied Mathematics

      Volume: 33 Issue: 2 Pages: 309-327

    • DOI

      10.1017/s0956792521000024

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Traveling wave dynamics for Allen-Cahn equations with strong irreversibility2022

    • Author(s)
      Akagi Goro、Kuehn Christian、Nakamura Ken-Ichi
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 375 Pages: 3173-3238

    • DOI

      10.1090/tran/8583

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 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 -2022

    • Author(s)
      赤木剛朗
    • Journal Title

      第 42 回発展方程式若手セミナー報告集(特別講演のサーベイ)

      Volume: 42 Pages: 1-39

    • Related Report
      2021 Annual Research Report
  • [Journal Article] Space-time arithmetic quasi-periodic homogenization for damped wave equations2022

    • Author(s)
      Oka Tomoyuki
    • Journal Title

      Results in Applied Mathematics

      Volume: 15 Pages: 100310-100310

    • DOI

      10.1016/j.rinam.2022.100310

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Existence of nodal solutions for the sublinear Moore-Nehari differential equation.2021

    • Author(s)
      R. Kajikiya
    • Journal Title

      Discrete and Continuous Dynamical Systems. Series A

      Volume: 41 Issue: 3 Pages: 1483-1506

    • DOI

      10.3934/dcds.2020326

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of the dissipative structure for the symmetric hyperbolic system with non-symmetric relaxation2021

    • Author(s)
      Ueda Yoshihiro
    • Journal Title

      Journal of Hyperbolic Differential Equations

      Volume: 18 Issue: 01 Pages: 195-219

    • DOI

      10.1142/s0219891621500053

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterization of dissipative structures for first-order symmetric hyperbolic system with general relaxation2021

    • Author(s)
      Yasunori Maekawa and Yoshihiro Ueda
    • Journal Title

      Mathematics

      Volume: 9 Issue: 7 Pages: 728-728

    • DOI

      10.3390/math9070728

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Comparison methods for a Keller--Segel-type model of pattern formations with density-suppressed motilities2021

    • Author(s)
      Fujie Kentarou、Jiang Jie
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 60 Issue: 3 Pages: 92-92

    • DOI

      10.1007/s00526-021-01943-5

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Cauchy problem for the Finsler heat equation2020

    • Author(s)
      G. Akagi, K. Ishige, R. Sato
    • Journal Title

      Adv. Calc. Var.

      Volume: 13 Issue: 3 Pages: 257-278

    • DOI

      10.1515/acv-2017-0048

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of positive radial solutions for a semipositone elliptic equation.2020

    • Author(s)
      R. Kajikiya and E. Ko
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 484 Issue: 2 Pages: 1-19

    • DOI

      10.1016/j.jmaa.2019.123735

    • NAID

      40022258055

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Decay structures for the equations of Porous elasticity in one-dimensional whole space2020

    • Author(s)
      Ramon Quintanilla, Yoshihiro Ueda
    • Journal Title

      Journal of Dynamics and Differential Equations

      Volume: 32 Issue: 4 Pages: 1669-1685

    • DOI

      10.1007/s10884-019-09767-w

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect2020

    • Author(s)
      Chun-Hsiung Hsia, Chang-Yeol Jung, Bongsuk Kwon, Yoshihiro Ueda
    • Journal Title

      Journal of Differential Equations

      Volume: 268 Issue: 12 Pages: 7897-7939

    • DOI

      10.1016/j.jde.2019.11.090

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Cauchy problem for thermoelastic plates with two temperatures2020

    • Author(s)
      Reinhard Racke, Yoshihiro Ueda
    • Journal Title

      Zeitschrift fur Analysis und ihre Anwendungen

      Volume: 39 Issue: 1 Pages: 103-129

    • DOI

      10.4171/zaa/1653

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Decay estimate and asymptotic profile for a plate equation with memory2020

    • Author(s)
      Yongqin Liu; Yoshihiro Ueda
    • Journal Title

      Journal of Differential Equations

      Volume: 268 Issue: 5 Pages: 2435-2463

    • DOI

      10.1016/j.jde.2019.09.007

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Global existence for a kinetic model of pattern formation with density-suppressed motilities2020

    • Author(s)
      Fujie Kentarou、Jiang Jie
    • Journal Title

      Journal of Differential Equations

      Volume: 269 Issue: 6 Pages: 5338-5378

    • DOI

      10.1016/j.jde.2020.04.001

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Asymptotic profiles for fast diffusion in bounded domains2024

    • Author(s)
      Goro Akagi
    • Organizer
      East Asia Workshop on Nonlinear Evolution Equations
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal rate of convergence to asymptotic profiles for fast diffusion in domains2024

    • Author(s)
      赤木剛朗
    • Organizer
      深江における非線形偏微分方程式研究集会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Time-fractional gradient flow に関する最近の進展2024

    • Author(s)
      赤木剛朗
    • Organizer
      第 2 回目白台非線形セミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Asymptotic profiles for fast diffusion in domains (ポスター発表)2024

    • Author(s)
      Goro Akagi
    • Organizer
      Turing Symposium on Morphogenesis, 2024 ― a Panorama in Turing's Sight ―
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Optimal rate of convergence to nondegenerate asymptotic profiles for fast diffusion in bounded domains2023

    • Author(s)
      Goro Akagi
    • Organizer
      Euro-Japanese Conference on Nonlinear Diffusion
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 特異拡散方程式の非退化な解の漸近形に対する収束レートの最適性について2023

    • Author(s)
      赤木剛朗
    • Organizer
      応用解析研究会 40 周年記念講演会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Evolution equations with complete irreversibility2023

    • Author(s)
      Goro Akagi
    • Organizer
      ICIAM 2023 Tokyo, Minisymposium ``Singular Problems in Mechanic''
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimality of the rate of convergence to asymptotic profiles for fast diffusion2023

    • Author(s)
      Goro Akagi
    • Organizer
      RIMS Satellite Seminar ``Homogenization and/or nonlocal operators''
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal rate of convergence to nondegenerate asymptotic profiles for fast diffusion in bounded domains2023

    • Author(s)
      赤木剛朗
    • Organizer
      九州函数方程式セミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Rates of convergence to asymptotic profiles for fast diffusion on domains2023

    • Author(s)
      Goro Akagi
    • Organizer
      SS65 ``Nonlinear Evolution Equations and Related Topics'', The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Gradient flow theory for time-dependent energies and applications to nonlinear PDEs2022

    • Author(s)
      赤木 剛朗(登壇者), 田中直樹
    • Organizer
      日本数学会 2021 年度年会, 実関数論分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Space-time periodic homogenization for the porous medium equation with nonnegative initial data2022

    • Author(s)
      赤木 剛朗, 岡 大将(登壇者)
    • Organizer
      日本数学会 2022 年度年会, 函数方程式分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] A framework for proving existence of local-energy solutions to doubly-nonlinear diffusion equations with growing initial data2021

    • Author(s)
      赤木剛朗
    • Organizer
      応用数学セミナー, 東北大学大学院理学研究科数学専攻
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Traveling wave dynamics for constrained Allen-Cahn equations2021

    • Author(s)
      Goro Akagi
    • Organizer
      The 46th Sapporo Symposium on Partial Differential Equations, 北海道大学大学院理学研究院数学部門
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 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-2021

    • Author(s)
      赤木剛朗
    • Organizer
      第 42 回発展方程式若手セミナー(特別講演)
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Rates of convergence to non-degenerate asymptotic profiles for fast diffusion equations via an energy method2021

    • Author(s)
      Goro Akagi
    • Organizer
      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)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Traveling wave dynamics for a one-dimensional constrained Allen-Cahn equation2021

    • Author(s)
      Goro Akagi
    • Organizer
      Asia-Pacific Analysis and PDE Seminar, The University of Sydney
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rates of convergence to non-degenerate asymptotic profiles for fast diffusion via energy methods2021

    • Author(s)
      赤木剛朗
    • Organizer
      研究集会「発展方程式の広がり:理論的基礎から実践的応用まで」, 京都大学数理解析研究所
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Energy method for quantitative analysis of rates of convergence to asymptotic profiles for fast diffusion2021

    • Author(s)
      Goro Akagi
    • Organizer
      PDE Seminars, The Hong Kong University of Science and Technology
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rates of convergence to asymptotic profiles for fast diffusion2021

    • Author(s)
      赤木剛朗
    • Organizer
      第 752 回『応用解析』研究会, 早稲田大学
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Rates of convergence to asymptotic profiles for fast diffusion2021

    • Author(s)
      赤木剛朗
    • Organizer
      NLPDEセミナー, 京都大学大学院理学研究科数学専攻
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Local well-posedness for some phase-field model of complete damage2021

    • Author(s)
      Goro Akagi
    • Organizer
      21st Conference of Continuum Mechanics Focusing on Singularities (CoMFoS21)(プレナリー)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On some quasistatic evolution equation with irreversibility and energy-conservation2021

    • Author(s)
      赤木 剛朗, 佐藤光汰朗(登壇者)
    • Organizer
      日本数学会 2022 年度秋季総合分科会, 函数方程式分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Qualitative space-time homogenization for the porous medium equation2021

    • Author(s)
      岡 大将(登壇者), 赤木 剛朗
    • Organizer
      日本数学会 2021 年度年会函数方程式分科会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Corrector results for space-time homogenization of nonlinear diffusion2021

    • Author(s)
      岡 大将(登壇者), 赤木 剛朗
    • Organizer
      日本数学会 2021 年度年会函数方程式分科会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Traveling wave dynamics for Allen-Cahn equations with strongly irreversibile constraints2020

    • Author(s)
      Goro Akagi
    • Organizer
      Nancy-Tohoku premeeting
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] Website of Goro Akagi

    • URL

      http://www.math.tohoku.ac.jp/~akagi/

    • Related Report
      2022 Annual Research Report
  • [Remarks] Achievements

    • URL

      http://www.math.tohoku.ac.jp/~akagi/achievement.html

    • Related Report
      2022 Annual Research Report
  • [Remarks] Webpage of Goro Akagi

    • URL

      http://www.math.tohoku.ac.jp/~akagi/

    • Related Report
      2021 Annual Research Report 2020 Annual Research Report
  • [Funded Workshop] Turing Symposium on Morphogenesis, 2024 -- a Panorama in Turing's Sight -- (on Feb 08-10, 2024 at Kawai Hall, Graduate School of Science, Tohoku University)2024

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Workshop on Degenerate and Singular Diffusion (on Oct 10-13, 2023 at ICMAT-UAM, Madrid)2023

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Euro-Japanese Conference on Nonlinear Diffusion (on Oct 16-20, 2023 at ICMAT-UAM, Madrid)2023

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] RIMS Workshop ``Evolution Equations and Related Topics -- Energy Structures and Quantitative Analysis --'' (Oct 02-04, 2023)2023

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Online lecture series by Prof. Daniele Hilhorst “Singular limit of deterministic and stochastic reaction-diffusion systems” (福泉麗佳氏, 義永那津人 氏と共同開催)2021

    • Related Report
      2021 Annual Research Report
  • [Funded Workshop] One-day Online Workshop on Chemotaxis(藤江健太郎)2021

    • Related Report
      2021 Annual Research Report

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Published: 2020-04-28   Modified: 2024-12-25  

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