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Analysis of the solution structure of non-linear partial differential equations corresponding to the wave phenomena and plasma phenomena

Research Project

Project/Area Number 21540186
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionThe University of Tokushima

Principal Investigator

ONO KOSUKE  徳島大学, 大学院ソシオ・アーツ・アンド・サイエンス研究部, 准教授 (00263806)

Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords準線形退化型波動方程式 / 非線形偏微分方程式 / dissipative wave / decay rate / Vlasov-Poisson system
Research Abstract

I conducted a study of mathematics relating to non-linear dissipative wave equations describing wave phenomena and Vlasov type equations describing plasma phenomena. I summarized the results of this research as academic papers and I published in magazines at home and abroad.For example, I got the results on the existence and uniqueness of global solutions and the asymptotic behaviors from the top and bottom of the solutions for degenerate quasi-linear hyperbolic partial differential equations to the initial boundary value problem. Further, I investigated on the conditions of the wave coefficient and the initial data for obtaining the results.

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (37 results)

All 2014 2013 2012 2011 2010 2009

All Journal Article (26 results) (of which Peer Reviewed: 16 results) Presentation (11 results)

  • [Journal Article] Global existence and decay properties of solutions for coupled degenerate dissipative hyperbolic systems of Kirchhoff type2014

    • Author(s)
      Kosuke Ono
    • Journal Title

      FUNKCIALAJ EKVACIOJ

      Volume: (印刷中)

    • NAID

      130004678001

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay estimates of solutions for mildly degenerate Kirchhoff type dissipative wave equations in unbounded domains2014

    • Author(s)
      Kosuke Ono
    • Journal Title

      Asymptotic Analysis

      Volume: Vol.88 Pages: 75-92

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lower decay estimates for non-degenerate dissipative wave equations of Kirchhoff type2014

    • Author(s)
      Kosuke Ono
    • Journal Title

      Scientiae Mathematicae Japonicae Online

      Volume: Vol.e-2014 Pages: 43-53

    • NAID

      130007643048

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On asymptotic behavior for degenerate hyperbolic equations with weak dissipation2013

    • Author(s)
      Kosuke Ono
    • Journal Title

      J. Math. Tokushima Univ

      Volume: Vol.47 Pages: 15-23

    • NAID

      110009789808

    • Related Report
      2013 Final Research Report
  • [Journal Article] On decay estimates of solutions for some degenerate nonlinear Kirchhoff strings with dissipation2013

    • Author(s)
      Kosuke Ono
    • Journal Title

      International Journal of Applied Mathematics

      Volume: Vol.26 Pages: 349-361

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions for mildly degenerate quasilinear hyperbolic equations2013

    • Author(s)
      Kosuke Ono
    • Journal Title

      Journal of Mathematical Sciences : Advances and Applications

      Volume: Vol.21 Pages: 39-48

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions for mildly degenerate quasilinear hyperbolic equations2013

    • Author(s)
      Kosuke Ono
    • Journal Title

      Journal of Mathematical Sciences: Advances and Applications

      Volume: 21

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On decay estimates of solutions for some degenerate nonlinear Kirchhoff strings with dissipation2013

    • Author(s)
      Kosuke Ono
    • Journal Title

      International Journal of Applied Mathematics(IJAM)

      Volume: 26

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On asymptotic behavior for degenerate hyperbolic equations with weak dissipation2013

    • Author(s)
      Kosuke Ono
    • Journal Title

      Journal of Mathematics, The University of Tokushima

      Volume: 47

    • NAID

      110009789808

    • Related Report
      2013 Annual Research Report
  • [Journal Article] On existence of global solutions for some mildly degenerate nonlinear Kirchhoff strings with linear dissipation2012

    • Author(s)
      Kosuke Ono
    • Journal Title

      J. Math. Tokushima Univ

      Volume: Vol.46 Pages: 13-22

    • NAID

      110009514567

    • Related Report
      2013 Final Research Report
  • [Journal Article] On existence of global solutions for some mildly degenerate nonlinear Kirchhoff strings with linear dissipation2012

    • Author(s)
      小野公輔
    • Journal Title

      Journal of Mathematics, The University of Tokushima

      Volume: 46

    • NAID

      110009514567

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Global existence and decay rate for a coupled degenerate hyperbolic system with dissipation2011

    • Author(s)
      Kosuke Ono
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: Vol.74 Pages: 1-13

    • NAID

      130007670076

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy decay for a dissipative wave equation with compactly supported data2011

    • Author(s)
      Kosuke Ono
    • Journal Title

      J. Math. Tokushima Univ

      Volume: Vol.45 Pages: 41-47

    • NAID

      110008729453

    • Related Report
      2013 Final Research Report
  • [Journal Article] Decay estimates for coupled degenerate hyperbolic system with strong damping2011

    • Author(s)
      Kosuke Ono
    • Journal Title

      International Journal of Applied Mathematics

      Volume: Vol.24 Pages: 383-392

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type2011

    • Author(s)
      Kosuke Ono
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Volume: Vol.34 Pages: 1339-1352

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On decay properties of solutions for degenerate strongly damped wave equations of Kirchhoff type2011

    • Author(s)
      Kosuke Ono
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: Vol.381 Pages: 229-239

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type2011

    • Author(s)
      小野公輔
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Volume: 34 Pages: 1339-1352

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Decay Properties of Solutions for Degenerate Strongly Damped Wave equations of Kirchhoff Type2011

    • Author(s)
      小野公輔
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 381 Pages: 229-239

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global Exlstence and Decay Rate for a Coupled Degenerate Hyperbolic System with Dissipation2011

    • Author(s)
      小野公輔
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 74 Pages: 1-13

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay Estimates for Coupled Degenerate Hyperbolic System with Strong Damping2011

    • Author(s)
      小野公輔
    • Journal Title

      International Journal of Applied Mathematics

      Volume: 24 Pages: 383-392

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Energy Decay for a dissipative wave equation with compactly supported data2011

    • Author(s)
      小野公輔
    • Journal Title

      Journal of Mathematics, The University of Tokushima

      Volume: 45 Pages: 41-47

    • NAID

      110008729453

    • Related Report
      2011 Annual Research Report
  • [Journal Article] On sharp decay estimates of solutions for mildly degenerate dissipative wave, equations of Kirchhoff type2011

    • Author(s)
      小野公輔
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Pages: 14-14

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A lower decay estimate for a degenerate Kirchhoff type wave equation with strong dissipation2010

    • Author(s)
      Kosuke Ono
    • Journal Title

      J. Math. Tokushima Univ

      Volume: Vol.44 Pages: 27-31

    • NAID

      110007870532

    • Related Report
      2013 Final Research Report
  • [Journal Article] A lower decay estimate for a degenerate Kirchhoff type wave equation with strong dissipation2010

    • Author(s)
      小野公輔
    • Journal Title

      Journal of Mathematics, The University of Tokushima

      Volume: 44 Pages: 27-31

    • NAID

      110007870532

    • Related Report
      2010 Annual Research Report
  • [Journal Article] On decay properties of solutions for the Vlasov--Poisson system2009

    • Author(s)
      Kosuke Ono
    • Journal Title

      J. Math. Tokushima Univ

      Volume: Vol.43 Pages: 25-30

    • NAID

      110007492239

    • Related Report
      2013 Final Research Report
  • [Journal Article] On decay properties of solutions for the Vlasov-Poisson system2009

    • Author(s)
      小野公輔
    • Journal Title

      Journal of Mathematics, The University of Tokushima 43

      Pages: 25-30

    • NAID

      110007492239

    • Related Report
      2009 Annual Research Report
  • [Presentation] Global solvability and decay estimates for mildly degenerate dissipative wave equations of Kirchhoff type2014

    • Author(s)
      小野公輔
    • Organizer
      2014日本数学会年会
    • Place of Presentation
      学習院大学(東京都)
    • Year and Date
      2014-03-16
    • Related Report
      2013 Final Research Report
  • [Presentation] On asymptotic behaviour for nondegenerate Kirchhoff type dissipative wave equations2014

    • Author(s)
      小野公輔
    • Organizer
      日本数学会中国四国支部例会
    • Place of Presentation
      島根大学(島根県)
    • Year and Date
      2014-01-26
    • Related Report
      2013 Final Research Report
  • [Presentation] On asymptotic behaviour for nondegenerate Kirchhoff type dissipative wave equations2014

    • Author(s)
      小野公輔
    • Organizer
      日本数学会中国四国支部例会
    • Place of Presentation
      島根大学(島根県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Global solvability and decay estimates for mildly degenerate dissipative wave equations of Kirchhoff type2014

    • Author(s)
      小野公輔
    • Organizer
      2014日本数学会年会
    • Place of Presentation
      学習院大学(東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On decay estimates for some degenerate nonlinear Kirchhoff strings with dissipation2013

    • Author(s)
      小野公輔
    • Organizer
      日本数学会中国四国支部例会
    • Place of Presentation
      高知大学(高知県)
    • Year and Date
      2013-01-27
    • Related Report
      2013 Final Research Report
  • [Presentation] On decay estimates for some degenerate nonlinear Kirchhoff strings with dissipation2013

    • Author(s)
      小野公輔
    • Organizer
      日本数学会中国四国支部例会
    • Place of Presentation
      高知大学理学部(高知県)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 退化した消散型波動方程式の時間大域的可解性と減衰評価式2012

    • Author(s)
      小野公輔
    • Organizer
      日本数学会中国四国支部例会
    • Place of Presentation
      岡山大学(岡山県)
    • Year and Date
      2012-01-22
    • Related Report
      2013 Final Research Report
  • [Presentation] 退化した消散型波動方程式の時間大域的可解性と減衰評価式2012

    • Author(s)
      小野公輔
    • Organizer
      日本数学会四国例会
    • Place of Presentation
      岡山大学環境理工学部(岡山県)
    • Year and Date
      2012-01-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Global Existence and Decay Estimates of Solutions for Mildly Degenerate Dissipative Wave Equations of Kirchhoff Type2011

    • Author(s)
      小野公輔
    • Organizer
      徳島数学談話会
    • Place of Presentation
      徳島大学(徳島県)
    • Year and Date
      2011-12-16
    • Related Report
      2013 Final Research Report
  • [Presentation] Global solvability and decay estimates for mildly degenerate dissipative wave equations of Kirchhoff type2011

    • Author(s)
      小野公輔
    • Organizer
      2011日本数学会年会
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2011-03-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Global solvability and decay estimates for mildly degenerate dissipative wave equations of Kirchhoff type2011

    • Author(s)
      小野公輔
    • Organizer
      日本数学会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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