• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Stability theory for the nonlinear partial differential equations with new dissipative structures

Research Project

Project/Area Number 17H07302
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Mathematical analysis
Research InstitutionTokyo University of Marine Science and Technology (2018)
Fukuoka Institute of Technology (2017)

Principal Investigator

Mori Naofumi  東京海洋大学, 学術研究院, 准教授 (10803413)

Research Collaborator Kawashima Shuichi  
Racke Reinhard  
Project Period (FY) 2017-08-25 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords非線形偏微分方程式 / 消散構造 / 安定性解析 / 緩和的双曲系 / Timoshenko 系 / Cattaneo 法則 / 時間大域解 / 減衰評価 / 解析学
Outline of Final Research Achievements

The Timoshenko system was considered by introducing Cattaneo's type heat conduction or memory, respectively. Consequently, their dissipative structures were well characterized and optimal decay estimates were shown. Besides, the global existence and uniqueness were obtained. Note that all of the results were proved under the minimal regularity assumption only on the small initial data.
Also, by generalized above results, the new stability condition was established, which could be applicable to more examples than any other condition.

Academic Significance and Societal Importance of the Research Achievements

新しい消散構造をもつ数理モデルの具体例には,身近で生活との関わりが深いものも多く含まれる。それにもかかわらず,これらのモデルに対しては統一的な解析方法が確立されておらず,しかも消散効果が脆弱なため,数学的に厳密に議論するのが難しいという問題点がある。
今回得られた研究成果は,今後,これらの数理モデルの統一的な解析方法の確立に向けた研究において必要不可欠の結果になると考えている。

Report

(3 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • Research Products

    (8 results)

All 2018 2017 Other

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

  • [Int'l Joint Research] コンスタンツ大学(ドイツ)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Global well-posedness and polynomial decay for a nonlinear Timoshenko?Cattaneo system under minimal Sobolev regularity2018

    • Author(s)
      Mori Naofumi、Racke Reinhard
    • Journal Title

      Nonlinear Analysis

      Volume: 173 Pages: 164-179

    • DOI

      10.1016/j.na.2018.03.019

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Dissipative structure and global existence in critical space for Timoshenko system of memory type2018

    • Author(s)
      Mori Naofumi
    • Journal Title

      Journal of Differential Equations

      Volume: 265 Issue: 4 Pages: 1627-1653

    • DOI

      10.1016/j.jde.2018.04.014

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] The S & K mixed condition for symmetric hyperbolic systems with non-symmetric relaxations2018

    • Author(s)
      N. Mori
    • Organizer
      2018年度日本数学会年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Mathematical analysis in the critical space for the nonlinear Timoshenko-Cattaneo system2017

    • Author(s)
      N. Mori, R. Racke
    • Organizer
      Kyushu Univ.-POSTECH-SJTU joint workshop on PDEs and related topics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Mathematical analysis for the nonlinear Timoshenko-Cattaneo system2017

    • Author(s)
      N. Mori, R. Racke
    • Organizer
      The sixth Japan-China Workshop on Mathematical Topics from Fluid Mechanics
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 股関節に可変剛性機構を有する受動歩行システムに用いる関節速度パターンの考察2017

    • Author(s)
      T. Sakata, H. Kino, M. Uemura, N. Mori, K. Murakami
    • Organizer
      第18回計測自動制御学会システムインテグレーション部門講演会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ナノシート液晶を用いたゲルアクチュエータの応答特性の基礎評価2017

    • Author(s)
      T. Kiyota, H. Kino, N. Miyamoto, T. Inatomi, T. Kato, H. Fujioka, N. Mori, K. Tahara)
    • Organizer
      第18回計測自動制御学会システムインテグレーション部門講演会
    • Related Report
      2017 Annual Research Report

URL: 

Published: 2017-08-25   Modified: 2020-03-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi