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Analysis on diffusion equations and nonlinear boundary conditions

Research Project

Project/Area Number 18K13435
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionFukuoka University (2021-2022)
The University of Tokyo (2020)
Tohoku University (2018-2019)

Principal Investigator

Sato Ryuichi  福岡大学, 理学部, 助教 (20802599)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords非線形拡散方程式 / 時間大域解 / 粘性解 / 非線形拡散 / 非線形境界条件 / 放物型方程式 / 解の爆発 / 多孔質媒質方程式 / 移流拡散 / 多孔質媒質 / 拡散方程式
Outline of Final Research Achievements

In this research we investigate nonlinear diffusion equations and the theory of existence of solutions. For the linear diffusion equations, there are many methods and solutions to consider some problems. However, for nonlinear diffusion equations, we have to choice correct solutions to treat such equations. We obtained some methods and new approachs to treat nonlinear diffusion equations. It can be expected that our results are applicable to expansive research.

Academic Significance and Societal Importance of the Research Achievements

本研究で得られた成果の立ち位置は非線形偏微分方程式の中でも最も基本的なものである.しかしながら,これらの成果は今後の研究で扱われるであろう諸問題を考察する際の指針になるものであり,学術的意義は十分にあるものと考えられる.実際,新たな解の存在手法を獲得したことで考察可能な問題設定は広がっているため,今まで考察されなかった問題も研究対象と認識され,研究が活発化すると期待している.本研究での成果が直ちに社会的に影響を与えることはないと考えられるが,将来的に大きな影響をもたらす研究につながる可能性は高い.

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (18 results)

All 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (1 results) Journal Article (5 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results) Presentation (12 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results)

  • [Int'l Joint Research] University of Rajshahi(バングラデシュ)

    • Related Report
      2021 Research-status Report
  • [Journal Article] Existence of Global-in-Time Solutions to a System of Fully Nonlinear Parabolic Equations2022

    • Author(s)
      Kosugi Takahiro、Sato Ryuichi
    • Journal Title

      Acta Applicandae Mathematicae

      Volume: 181 Issue: 1 Pages: 1-24

    • DOI

      10.1007/s10440-022-00533-7

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces2021

    • Author(s)
      Md. Rabiul Haque, Norisuke Ioku, Takayoshi Ogawa, Ryuichi Sato.
    • Journal Title

      Differenrial Integral Equations

      Volume: 34 Pages: 223-244

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Existence of weak solutions to a convection diffusion equation in a uniformly local lebesgue space2020

    • Author(s)
      Rabiul Haque Md., Mathematical Institute, Tohoku University, Sendai 980-8578, Japan、Ogawa Takayoshi、Sato Ryuichi、,Mathematical Institute/Research Alliance Center of Mathematical Science, Tohoku University, Sendai 980-8578, Japan
    • Journal Title

      Communications on Pure & Applied Analysis

      Volume: 19 Issue: 2 Pages: 677-697

    • DOI

      10.3934/cpaa.2020031

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Existence of solutions to the slow diffusion equation with a nonlinear source2020

    • Author(s)
      Sato Ryuichi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 484 Issue: 2 Pages: 123721-123721

    • DOI

      10.1016/j.jmaa.2019.123721

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Critical exponents for the fast diffusion equation with a nonlinear boundary condition2020

    • Author(s)
      Sato Ryuichi、Takahashi Jin
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 482 Issue: 1 Pages: 123526-123526

    • DOI

      10.1016/j.jmaa.2019.123526

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] Existence of global-in-time solutions to a system of fully nonlinear parabolic equations2022

    • Author(s)
      Ryuichi Sato
    • Organizer
      RIMS研究集会, 偏微分方程式の臨界現象と正則性理論及び漸近解析
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] On existence of solutions to a system of fully nonlinear parabolic equations2022

    • Author(s)
      佐藤龍一
    • Organizer
      日本数学会2022年度年会
    • Related Report
      2021 Research-status Report
  • [Presentation] Existence of solutions to the slow diffusion equation with a nonlinear source2022

    • Author(s)
      Ryuichi Sato
    • Organizer
      青葉山勉強会(第16回) “Reaction-Diffusion Equations”
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 完全非線形放物型連立系の時間大域解の存在2021

    • Author(s)
      佐藤龍一
    • Organizer
      九州関数方程式セミナー
    • Related Report
      2021 Research-status Report
  • [Presentation] Existence of solutions to the slow diffusion equation with a nonlinear source2021

    • Author(s)
      佐藤龍一
    • Organizer
      第253回広島数理解析セミナー
    • Related Report
      2021 Research-status Report
  • [Presentation] Existence of solutions to the slow diffusion equation with a nonlinear source2020

    • Author(s)
      Ryuichi Sato
    • Organizer
      福岡大学解析セミナー
    • Related Report
      2020 Research-status Report
  • [Presentation] Existence of solutions to a nonlinear diffusion equation in uniformly local Lebesgue space2020

    • Author(s)
      Ryuichi Sato
    • Organizer
      福岡大学理学部応用数学科 談話会
    • Related Report
      2020 Research-status Report
  • [Presentation] 非線形境界条件付き拡散方程式の解の存在と爆発2020

    • Author(s)
      Ryuichi Sato
    • Organizer
      第10回非線形発展方程式セミナー@KUE
    • Related Report
      2020 Research-status Report
  • [Presentation] Existence of solutions to the slow diffusion equation with a nonlinear source2019

    • Author(s)
      佐藤龍一
    • Organizer
      第166回神楽坂解析セミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] Existence of solutions to the slow diffusion equation with a nonlinear source2019

    • Author(s)
      佐藤龍一
    • Organizer
      偏微分方程式セミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] Local and global existence of slow diffusion equation with a nonlinear source2019

    • Author(s)
      佐藤龍一
    • Organizer
      2019年日本数学会年会
    • Related Report
      2018 Research-status Report
  • [Presentation] Global existence in critical space for a nonlinear diffusion equation with a nonlinear source2018

    • Author(s)
      Ryuichi Sato
    • Organizer
      The AIMS Conference series on dynamical systems and differential equations, Asymptotics for Nonlinear Diffusion Equations and Related Topics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research

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Published: 2018-04-23   Modified: 2024-01-30  

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