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A study on asymptotic behavior of solutions for evolution equations

Research Project

Project/Area Number 14540208
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

IKEHATA Ryo  Hiroshima University, Graduate School of Education, Associate Professor, 大学院・教育学研究科, 助教授 (10249758)

Co-Investigator(Kenkyū-buntansha) KAWASHITA Mishio  Hiroshima University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80214633)
小林 孝行  九州工業大学, 工学部, 助教授 (50272133)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥500,000 (Direct Cost: ¥500,000)
KeywordsWave equation / exterior domain / Energy / decay / asymptotics of solutions / 外部問題 / エネルギー減衰 / 消散項 / 非有界領域 / 臨界指数 / 減衰評価
Research Abstract

We first discussed the possibility of applications of the device due to Ikehata-Matsuyama (which was newly developed in 1999) to some evolution equations in unbounded domains. For this we have obtained several results concerning the global well-posedness result of damped wave equations with the Fujita type power nonlinearity. And also by the device we have obtained the new result concerning the diffusion phenomenon of abstract second-order evolution equations.
Second we have found the new decay estimates of (semilinear) damped wave equations, which are dealt with in the N-dimensional half space.
Third, by the two methods due to Ikehata-Matsuyama above and Todorova-Yordanov we have succeeded in removing the compactness of the support on the initial data in order to obtain local energy decay estimates of the wave equation in an exterior domain with a star-shaped complement. This result completely generalizes that obtained by Morawetz in 1961. It should be pointed out that the method used to derive local enegy decay results has many wide applications to hyperbolic equations in exterior domains.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (21 results)

All 2005 2004 Other

All Journal Article (11 results) Publications (10 results)

  • [Journal Article] Two dimensional exterior mixed problem for semilinear damped wave equations2005

    • Author(s)
      R.IKEHATA
    • Journal Title

      J.Math.Anal.Appl. 301

      Pages: 360-371

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Local energy decay for linear wave equations with variable coefficients2005

    • Author(s)
      R.IKEHATA
    • Journal Title

      J.Math.Anal.Appl. 306

      Pages: 330-348

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Local energy decay for linear wave equations with localized dissipation2005

    • Author(s)
      R.IKEHATA
    • Journal Title

      Funkcial.Ekvac. (印刷中)

    • NAID

      130000141320

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Local energy decay for linear wave equations with variable coefficients2005

    • Author(s)
      R.IKEHATA
    • Journal Title

      J.Math.Anal.Appl. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Global existence of solutions for semilinear damped wave equations in R^{N} with non-compactly supported initial data2005

    • Author(s)
      R.IKEHATA, K.TANIZAWA
    • Journal Title

      Nonlinear Anal. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] New decay estimates for linear damped wave equations and its application to nonlinear problem2004

    • Author(s)
      R.IKEHATA
    • Journal Title

      Math.Meth.Appl.Sci. 27

      Pages: 865-889

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Decay estimates of solutions for dissipative wave equations in R^{N} with lower power nonlinearities2004

    • Author(s)
      R.IKEHATA
    • Journal Title

      J.Math.Soc.Japan 56

      Pages: 365-373

    • NAID

      10013122934

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Local energy decay for linear wave equations with non-compactly supported initial data2004

    • Author(s)
      R.IKEHATA
    • Journal Title

      Math.Meth.Appl.Sci. 27

      Pages: 1881-1892

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] New decay estimates for linear damped wave equations and its application to nonlinear problem2004

    • Author(s)
      R.IKEHATA
    • Journal Title

      Math.Methods Appl.Sci. 27

      Pages: 865-889

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Local energy decay for linear wave equations with non-compactly supported initial data2004

    • Author(s)
      R.IKEHATA
    • Journal Title

      Math.Methods Appl.Sci. 27

      Pages: 1881-1892

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Global existence of solutions for semilinear damped wave equation in 2-D exterior domain2004

    • Author(s)
      R.IKEHATA
    • Journal Title

      J.Diff.Eqns 200

      Pages: 53-68

    • Related Report
      2004 Annual Research Report
  • [Publications] Ryo IKEHATA: "Critical exponent for semilinear damped wave equations in the N-dimensional half space"J.Math.Anal.Appl.. 288. 803-818 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Ryo IKEHATA: "New decay estimates for linear damped wave equations and its application to nonlinear problem"Math.Methods in the Appl.Sci.. In press.

    • Related Report
      2003 Annual Research Report
  • [Publications] Ryo IKEHATA: "Global existence of solutions for semilinear damped wave equation in 2-D exterior domain"J.Differential Equations. In press.

    • Related Report
      2003 Annual Research Report
  • [Publications] Ryo IKEHATA: "Local energy decay for linear wave equations with non-compactly supported initial data"Math.Methods in the Appl.Sci.. In press.

    • Related Report
      2003 Annual Research Report
  • [Publications] Ryo IKEHATA: "L^2-behaviour of solutions to the linear heat and wave equations in an exterior domains"Sci. Math. Japonicae. 55. 33-42 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ryo IKEHATA: "Critical exponents for semilinear dissipative wave equations in IR^N"J. Math. Anal. Appl.. 269. 87-97 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ryo IKEHATA: "Small Data Global Existence of Solutions for Dissipative Wave Equations in an Exterior Domain"Funkcial. EKvac.. 45. 259-269 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ryo IKEHATA: "Diffusion Phenomenon for linear dissipative wave equations in unbounded domains"J. Diff. Equations. 186. 633-651 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Ryo IKEHATA: "Decay estimates of solutions for dissipative wave equations in IR^N with lower power nonlinearities"J. Math. Soc. Japan. (近刊).

    • Related Report
      2002 Annual Research Report
  • [Publications] Ryo IKEHATA: "Diffusion phenomenon for second order linear evolution equations"Studia Math.. (近刊).

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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