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

2012 Fiscal Year Final Research Report

Structure of the solutions to the system ofcompressible fluid

Research Project

  • PDF
Project/Area Number 22540202
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSaga University

Principal Investigator

KOBAYASHI Takayuki  佐賀大学, 大学院・工学系研究科, 教授 (50272133)

Co-Investigator(Kenkyū-buntansha) KAJIKIYA Ryuji  佐賀大学, 大学院・工学系研究科, 教授 (10183261)
Co-Investigator(Renkei-kenkyūsha) KAGEI Yoshiyuki  九州大学, 大学院・数理学研究院, 教授 (80243913)
MISAWA Masashi  熊本大学, 大学院・自然科学研究科, 教授 (40242672)
IKEHATA Ryo  広島大学, 教育学研究科, 教授 (10249758)
Project Period (FY) 2010 – 2012
Keywords関数方程式
Research Abstract

We consider the initial boundary value problems for the semilinear damped wave equations and the semilinear heat equations in two dimension exterior domains. We give the L2 boundedness with respect to the space and time valuables of thesolutions. Also,we consider the zero relaxation time approximation to the compressible Navier-Stokes-Poisson system to derive the mono-polar drift-diffusion system of degenerated type in a framework of the theory of weak solution.

  • Research Products

    (29 results)

All 2012 2011 2010 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (18 results)

  • [Journal Article] Non-radial least energy solutions of the generalized H¥'{e}non equation.2012

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Differential Equations

      Volume: 252, No.2 Pages: 1987-2003

    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow2012

    • Author(s)
      Y. Kagei
    • Journal Title

      Arch. Rational Mech. Anal

      Volume: Vol. 205, no. 2 Pages: 585-650

    • Peer Reviewed
  • [Journal Article] Energy decay estimates for wave equations with a fractional damping2012

    • Author(s)
      R. Ikehata, and M.Natsume
    • Journal Title

      Differential and Integral Eqns

      Volume: 25, No.9-10 Pages: 939-956

    • Peer Reviewed
  • [Journal Article] Decay Property for the linear wave equations in two dimensional exterior domains.2011

    • Author(s)
      M. Misawa, S. Okamura and T. Kobayashi
    • Journal Title

      Differential and Integral Equations

      Volume: 63, No.1 Pages: 263-294

    • Peer Reviewed
  • [Journal Article] Sublinear elliptic equations with singular coefficients on the boundar2011

    • Author(s)
      R. Kajikiya
    • Journal Title

      J. Math. Soc. Japan

      Volume: 63, No.1 Pages: 263-294

    • Peer Reviewed
  • [Journal Article] Global existence of solutions to the compressible Navier-Stokes equation around parallel flows2011

    • Author(s)
      Y. Kagei
    • Journal Title

      J. Differential Equations

      Volume: vol. 251 Pages: 3248-3295

    • Peer Reviewed
  • [Journal Article] Energy decay rates of elastic waves in unbounded domain with potential type of damping2011

    • Author(s)
      R.C.Charaon and R. Ikehata
    • Journal Title

      J. Math. Anal. Appl

      Volume: 380, No.5 Pages: 46-56

    • Peer Reviewed
  • [Journal Article] Superlinear elliptic equations with singular coefficients on the boundary2010

    • Author(s)
      R. Kajikiya
    • Journal Title

      Nonlinear Analysis, T.M.A

      Volume: 73, No.7 Pages: 2117-2131

    • Peer Reviewed
  • [Journal Article] Local energy decay for a class of hyperbolic equations with constant coefficients near infinity2010

    • Author(s)
      S.Aikawa and R. Ikehata
    • Journal Title

      Math. Nachr

      Volume: 283, No.5 Pages: 636-647

    • Peer Reviewed
  • [Journal Article] Fluid Mechanical Approximation to the Degenerated Drift-Diffusion System from Compressible Navier-Stokes-Poisson system

    • Author(s)
      T. Kobayashi and T. Ogawa
    • Journal Title

      Indiana University Mathematics Journal

    • Peer Reviewed
  • [Journal Article] L2 boundedness for the 2D exterior problems for the semilinear heat and dissipative wave equations

    • Author(s)
      T. Kobayashi and M. Misawa
    • Journal Title

      Rims Kokyuroku Bessatsu: Harmonic Analysis and Nonlinear Partial Differential Equations. eds. T. Ozawa, M. Sugimoto

    • Peer Reviewed
  • [Presentation] Non-radial positive solutions of the H¥'{e}non equation2012

    • Author(s)
      R. Kajikiya
    • Organizer
      International Symposium on Nonlinear Analysis and Optimization 2012
    • Place of Presentation
      Pukyong National University, Pusan, Korea
    • Year and Date
      20120208-10
  • [Presentation] Asymptotic behavior of solutions of the compressible Navier-Stokes equation around parallel flows2012

    • Author(s)
      Y. Kagei
    • Organizer
      2012 Fall Trimester Applied Math Colloquium
    • Place of Presentation
      School of Technology Management Ulsan National Institute of Science and Technology (UNIST), Ulsan, Republic of Korea
    • Year and Date
      2012-11-15
  • [Presentation] A regularity for nonlinear parabolic systems of p-Laplacian type with critical growth2012

    • Author(s)
      M. Misawa
    • Organizer
      アールト大学数学解析セミナー
    • Place of Presentation
      アールト大学, Helsinki, Finland
    • Year and Date
      2012-09-11
  • [Presentation] L2 boundedness for the solutions to the 2D Navies-Stokes equations2012

    • Author(s)
      T. Kobayashi
    • Organizer
      Parabolic and Navier-Stokes Equations
    • Place of Presentation
      Banach center, Bedlewo, Poland
    • Year and Date
      2012-09-06
  • [Presentation] L2 boundedness of solutions for the 2D semilinear dissipative wave equations2012

    • Author(s)
      T. Kobayashi
    • Organizer
      RIMS 研究集会「調和解析と非線形偏微分方程式」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-07-04
  • [Presentation] Energy decay estimates for wave equations with a fractional dampin2012

    • Author(s)
      R. Ikehata
    • Organizer
      第9回 AIMS International Conference on dynamical Systems, Differential equations and Applications
    • Place of Presentation
      Hyatt Regency Grand Cypress, Orlando, Florida, USA
    • Year and Date
      2012-07-04
  • [Presentation] Weighted Lp theory for the Stokes resolvent in some unbounded domains2011

    • Author(s)
      T. Kobayashi
    • Organizer
      第4回 日独流体数学国際研究集会
    • Place of Presentation
      早稲田大学
    • Year and Date
      20111128-1202
  • [Presentation] Existence of non-radial solutions for the generalized H¥'{e}non equation2011

    • Author(s)
      R. Kajikiya
    • Organizer
      2011 International Workshop on Nonlinear PDE and Applications
    • Place of Presentation
      Pusan National University, Pusan, Korea
    • Year and Date
      20110620-24
  • [Presentation] On the stability of parallel flows of the compressible Navier-Stokes equation2011

    • Author(s)
      Y. Kagei
    • Organizer
      The 3rd Kyushu University-POSTECH Joint Workshop - Partial Differential Equations and Fluid Dynamics
    • Place of Presentation
      POSTECH, Pohang, Korea
    • Year and Date
      20110616-17
  • [Presentation] 空間遠方で臨界減衰する摩擦項を持つ波動方程式のエネルギー減衰についての新展開2011

    • Author(s)
      R. Ikehata
    • Organizer
      日本数学会秋季総合分科会函数方程式論分科会(特別講演)
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
  • [Presentation] Decay property of solutions to the 2D Wave equations with damping terms or strong damping terms2011

    • Author(s)
      T. Kobayashi
    • Organizer
      Pohang-Kyushu workshop on Partial Differential Equations.
    • Place of Presentation
      POSTECH, Pohang, 韓国
    • Year and Date
      2011-06-17
  • [Presentation] Weighted estimates of the solutions to the Navier-Stokes equations in half space and perturbed half-space2011

    • Author(s)
      T. Kobayashi
    • Organizer
      Workshop on Applied Mathematics Euskadi-Kyushu 2011
    • Place of Presentation
      Basque Center for Applied Mathematics, Spain
    • Year and Date
      2011-03-10
  • [Presentation] Stability of solutions for fast diffusion equations2010

    • Author(s)
      R. Kajikiya
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      京都大学
    • Year and Date
      20101218-19
  • [Presentation] symptotic behavior of solutions of the compressible Navier-Stokes equation around a parallel flow2010

    • Author(s)
      Y. Kagei
    • Organizer
      13th International Conference on Hyperbolic Problems: Theorym Numerics, Applications
    • Place of Presentation
      Beijing, China
    • Year and Date
      20100615-19
  • [Presentation] Weighted Lp-Lq estimates for the Stokes semigroup in some unbounded domains2010

    • Author(s)
      T.Kobayashi
    • Organizer
      Weighted Lp-Lq estimates for the Stokes semigroup in some unbounded domains
    • Place of Presentation
      芝蘭会館別館, 京都
    • Year and Date
      2010-11-16
  • [Presentation] Weighted estimates for the Stokes semigroup in half space and perturbed half-space2010

    • Author(s)
      T. Kobayashi
    • Organizer
      Regularity aspects of PDE - a week for Wojciech Zajaczkowski
    • Place of Presentation
      Banach center,Bedlewo,Poland
    • Year and Date
      2010-09-11
  • [Presentation] 時間発展 p 調和方程式系に対するヘルダー評価について2010

    • Author(s)
      M. Misawa
    • Organizer
      奈良女子大学偏微分方程式研究集会
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2010-06-27
  • [Presentation] Conference on dynamical Systems2010

    • Author(s)
      R. Ikehata
    • Organizer
      Differential equations and Applications
    • Place of Presentation
      Dresden University of Technology, Dresden, Germany
    • Year and Date
      2010-05-27

URL: 

Published: 2014-08-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi