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2010 Fiscal Year Final Research Report

Research of global behavior of classical solutions for quasilinear Wave equations

Research Project

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Project/Area Number 20540206
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionShizuoka University

Principal Investigator

HOSHIGA Akira  Shizuoka University, 工学部, 准教授 (60261400)

Co-Investigator(Kenkyū-buntansha) KATAYAMA Soichiro  和歌山大学, 教育学部, 教授 (70283942)
KUBO Hideo  東北大学, 情報科学研究科, 教授 (50283346)
KUROKAWA Yuki  米子工業高等専門学校, 一般科目, 講師 (50375375)
Project Period (FY) 2008 – 2010
Keywords波動方程式 / 零条件 / ライフスパン
Research Abstract

In this study, we succeeded in the classification of the sufficient conditions (null-conditions) for the global existence of the classical solutions to the system of nonlinear wave equations in 2 and 3 space dimensions, according to the type of the nonlinear terms (Null-form type, Non-resonance type and Nonlinear dissipation type). As development of the research, we also obtained precise evaluations to the lifespan of the classical solutions for the first order hyperbolic PDE systems with multiple propagation speeds and for the nonlinear elastic wave equations.

  • Research Products

    (11 results)

All 2011 2010 2009 2008 Other

All Journal Article (5 results) Presentation (5 results) Remarks (1 results)

  • [Journal Article] The lifespan of solutions to quasilinear hyperbolic systems of n×n in the critical case2010

    • Author(s)
      Akira Hoshiga, Taiichi Nose
    • Journal Title

      Saitama Mathematical Journal vol.26.

      Pages: 15-38

  • [Journal Article] On the large time behavior of solutions to semilinear system of the wave equation2009

    • Author(s)
      Soichiro Katavama, Hideo Kubo
    • Journal Title

      Proceedings of the 5th International ISAAC congress vol.1.

      Pages: 581-589

  • [Journal Article] The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2 dimensional space2008

    • Author(s)
      Akira Hoshiga
    • Journal Title

      Hokkaido Mathematical Journal 37

      Pages: 669-688

  • [Journal Article] An alternative proof of global existence for nonlinear wave equations in an exterior domain2008

    • Author(s)
      Soichiro Katavama, Hideo Kubo
    • Journal Title

      Journal of the Mathematical Society of Japan 60

      Pages: 1135-1170

  • [Journal Article] Global existence and asymptotic behavior of solutions to systems of semilinear wave equations in two space dimensions2008

    • Author(s)
      Soichiro Katavama
    • Journal Title

      Hokkaido Mathematical Journal 37

      Pages: 689-714

  • [Presentation] Lower bounds for the lifespanof solutions to nonlinear wave quations inelasticity2011

    • Author(s)
      久保英夫
    • Organizer
      名古屋偏微分方程式研究集会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2011-02-15
  • [Presentation] On the asymptotic behavior for elastic waves2010

    • Author(s)
      久保英夫
    • Organizer
      The 8th Workshop on Linear and Nonlinear Waves
    • Place of Presentation
      大阪大学
    • Year and Date
      2010-09-12
  • [Presentation] Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions2010

    • Author(s)
      片山聡一郎
    • Organizer
      偏微分方程式姫路研究集会
    • Place of Presentation
      イーグレ姫路
    • Year and Date
      2010-02-23
  • [Presentation] The lifespan of solutions to quasilinear hyperbolic systems in the critical case2008

    • Author(s)
      野瀬泰一, 星賀彰
    • Organizer
      第8回浜松偏微分方程式研究集会
    • Place of Presentation
      静岡大学
    • Year and Date
      2008-12-22
  • [Presentation] 非線形波動方程式系の大域解の存在とnull条件について2008

    • Author(s)
      片山聡一郎
    • Organizer
      日本数学会2008年度秋季総合分科会(特別講演)
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
  • [Remarks] ホームページ等

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Published: 2012-01-26   Modified: 2016-04-21  

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