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Time global structure of solutions of nonlinear conservation law with viscosity and relaxation

Research Project

Project/Area Number 19340037
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

MATSUMURA Akitaka  Osaka University, 大学院・情報科学研究科, 教授 (60115938)

Co-Investigator(Kenkyū-buntansha) CHAWANYA Takeshi  大阪大学, 大学院・情報科学研究科, 准教授 (80294148)
小田中 紳二  大阪大学, サイバーメディアセンター, 教授 (20324858)
西原 健二  早稲田大学, 政治経済学部, 教授 (60141876)
西畑 伸也  東京工業大学, 大学院・情報理工学研究科, 准教授 (80279299)
柳沢 卓  奈良女子大学, 人間文化研究科, 准教授 (30192389)
柘植 直樹  広島工業大学, 情報学部, 講師 (30449897)
Co-Investigator(Renkei-kenkyūsha) ODANAKA Shinji  大阪大学, サイバーメディアセンター, 教授 (20324858)
NISHIHARA Kenji  早稲田大学, 政治経済学部, 教授 (60141876)
NISHIBATA Shinya  東京工業大学, 大学院・情報理工学研究科, 教授 (80279299)
YANAGISAWA Taku  奈良女子大学, 大学院・自然科学研究科, 教授 (30192389)
KOMATSU Gen  大阪大学, 大学院・理学研究科, 准教授 (60108446)
TSUGE Naoki  岐阜大学, 教育学部, 准教授 (30449897)
IOHARA Takao  大阪大学, 大学院・理学研究科, 助教 (00294140)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥11,960,000 (Direct Cost: ¥9,200,000、Indirect Cost: ¥2,760,000)
Fiscal Year 2010: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2008: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2007: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Keywords保存則 / 時間大域解 / 長時間挙動 / ナヴィエ・ストークス方程式 / 半導体方程式 / 接触不連続 / 希薄波 / 漸近挙動 / 半導体の程式 / 定常解 / 大自由度力学系 / 解の存在と一意性 / 粘性保存則系 / 粘性衝撃波 / 大自由度カオス / ドリフト拡散モデル / フォッカー・プランク・ボルツマン方程式 / 漸近安定 / 接触不連続解 / 半導体 / 量子流体力学モデル / 粘性保存則 / 消散型波動方程式 / 漸近安定性 / 量子ドリフト-拡散方程式 / オイラー方程式
Research Abstract

Several new weighted energy methods were successfully proposed to have a priori estimates of solutions. With the aid of these methods, has been much progressed the analysis on the large time behaviors of the solutions of scalar viscous conservation law with non-convex flux, system of equations of viscous ideal gas, dissipative wave equations, etc. Also for model equations of semiconductor, the analysis on existence, uniqueness and asymptotic stability of stationary solutions, hierarchy structures with respect to several physical parameters, and methods of numerical computation has been much progressed.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (48 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (24 results) (of which Peer Reviewed: 24 results) Presentation (24 results)

  • [Journal Article] Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity2010

    • Author(s)
      A. Matsumura, Y. Wang
    • Journal Title

      Met.Appl.Anal. 17

      Pages: 279-290

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of viscous contact wave with rarefaction waves for one-dimensional compressible Navier-Stokes system2010

    • Author(s)
      F. Huang, J. Li, A. Matsumura
    • Journal Title

      Arch.Ration.Mech.Anal. 197

      Pages: 89-116

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A minimal system with a depth-two heteroclinic network2010

    • Author(s)
      T. Chawanya, P. Ashwin
    • Journal Title

      Dynamical Systems 25

      Pages: 397-412

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relaxation limit and initial layer to hydrodynamic models for semiconductors2010

    • Author(s)
      S. Nishibata, M. Suzuki
    • Journal Title

      Journal of Differential Equations 249

      Pages: 1385-1409

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors2010

    • Author(s)
      N. Tsuge
    • Journal Title

      Nonlinear Anal. 73

      Pages: 779-787

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of viscous contact wave with rarefaction waves for one-dimensional compressible Navier-Stokes system2010

    • Author(s)
      F.Huang, J.Li, A.Matsumura
    • Journal Title

      Arch.Ration.Mech.Anal.

      Volume: 197 Pages: 89-116

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal decay rate of the compressible Navier-Stokes-Poisson system in R^32010

    • Author(s)
      H.Li, A.Matsumura, G.Zhang
    • Journal Title

      Arch.Ration.Mech.Anal.

      Volume: 196 Pages: 681-713

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A minimal system with a depth-two heteroclinic network2010

    • Author(s)
      T.Chawanya, P.Ashwin
    • Journal Title

      Dynamical Systems

      Volume: 25 Pages: 397-412

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation2009

    • Author(s)
      F. Huang, A. Matsumura
    • Journal Title

      Commun.Math.Phys. 289

      Pages: 841-861

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of a stationary solution2009

    • Author(s)
      S. Nishibata, M. Suzuki
    • Journal Title

      Arch.Rational Mech.Anal. 192

      Pages: 187-215

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonhomogeneous boundary value problems for stationary Navier-Stokes equations in a multiply connected domain2009

    • Author(s)
      H. Kozono, T. Yanagisawa
    • Journal Title

      Pacific Journal of Mathematics 243

      Pages: 127-150

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of a stationary solution to a heat-conductive hydrodynamic model for semiconductors2009

    • Author(s)
      S. Nishibata, M. Suzuki
    • Journal Title

      Arch. Rat. Mech. Anal. 192

      Pages: 187-215

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation2009

    • Author(s)
      F. Huang, A. Matsumura
    • Journal Title

      Commun. Math. Phys. 289

      Pages: 841-861

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation2009

    • Author(s)
      F.Huang, A.Matsumura
    • Journal Title

      Commun.Math.Phys. 289

      Pages: 841-861

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A numerical method for a transient quantum drift-diffusion model arising semiconductor devices2008

    • Author(s)
      T. Shimada, S. Odanaka
    • Journal Title

      Journal of Computational Electronics 7

      Pages: 485-493

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A numerical method for a transient quantum drift-diffusion model arising semiconductor devices2008

    • Author(s)
      T. Shimada, S. Odanaka
    • Journal Title

      Journal of Computational Electronics vol. 7

      Pages: 485-493

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Behavior of the Fokker-Planck-Boltzmann equation near a Maxwellian2008

    • Author(s)
      H. -L. Li, A. Matsumura
    • Journal Title

      Arch. Ration. Mech. Anal. 189

      Pages: 1-44

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large-time behavior of solutions to an initial-boundary value problem on the half line for scalar viscous conservation law2007

    • Author(s)
      Hashimoto, A. Matsumura
    • Journal Title

      Met.Appl.Anal. 14

      Pages: 45-60

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Large-time behavior of solutions to an initial-boundary value problem on the half line for scalar viscous conservation law2007

    • Author(s)
      I. Hashimoto and A. Matsumura
    • Journal Title

      Methods and Applications of Analysis 14

      Pages: 45-60

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Adaptive time discretization for a transient quantum drift-diffusion model2007

    • Author(s)
      T. Shimada and S. Odanaka
    • Journal Title

      Proceedings of International Conference of Simulation of Semiconductor Processes and Devices

      Pages: 337-340

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions for the damped wave equation with slowly decaying data2007

    • Author(s)
      T. Narazaki and K. Nishihara
    • Journal Title

      J. Math. Anal. Appl. 338

      Pages: 803-819

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence rates toward the stationary solution for the compressible Navier-Stokes equation in half space2007

    • Author(s)
      T. Nakamura, S. Nishibata and T. Yuge
    • Journal Title

      Journal of Differential Equations 241

      Pages: 94-111

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of a stationary solution to a hydrodynamic model for semiconductors2007

    • Author(s)
      S. Nishibata and M. Suzuki
    • Journal Title

      Osaka Journal of Mathematics 44

      Pages: 639-665

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to the viscous Burgers equation2007

    • Author(s)
      T. Yanagisawa
    • Journal Title

      Osaka Journal of Mathematics 44

      Pages: 99-119

    • NAID

      120004840827

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity2011

    • Author(s)
      松村昭孝
    • Organizer
      第28回九州における偏微分方程式研究集会
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2011-01-26
    • Related Report
      2010 Final Research Report
  • [Presentation] Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity2011

    • Author(s)
      松村昭孝
    • Organizer
      第28回九州における偏微分方程式研究集会
    • Place of Presentation
      九州大学 西新プラザ(招待講演)
    • Year and Date
      2011-01-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] 3次元系における階層的構造を持つヘテロクリニックネットワーク2010

    • Author(s)
      茶碗谷毅
    • Organizer
      日本物理学会2010年秋季大会
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2010-09-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] 部分的に線形退化する流束を持つ単独粘性保存則に対する初期値問題の時間大域解の漸近挙動2010

    • Author(s)
      吉田夏海、松村昭孝
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic behavior of solutions to the Euler-Poisson equation in plasma physics2010

    • Author(s)
      西畑伸也
    • Organizer
      Pacific Rim Conference
    • Place of Presentation
      Stanford university, U.S.A
    • Year and Date
      2010-06-30
    • Related Report
      2010 Final Research Report
  • [Presentation] Large time behavior of solutions to the Cauchy problem for the semilinear damped wave equation2010

    • Author(s)
      西原健二
    • Organizer
      2010 Chinese-German conference on fluid and gas dynamics
    • Place of Presentation
      Zhejiang Normal University, Jinhua, China
    • Year and Date
      2010-05-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Helmholtz-Weyl分解とその応用2010

    • Author(s)
      柳沢卓
    • Organizer
      日本数学会特別講演
    • Place of Presentation
      慶応義塾大学矢上キャンパス
    • Year and Date
      2010-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] 一次元粘性保存則系の解の長時間挙動---粘性気体の方程式系を軸に---2009

    • Author(s)
      松村昭孝
    • Organizer
      数理解析研究所研究集会「非線形波動現象の数理と応用」
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-10-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] 圧縮性オイラー方程式の時間大域解と漸近挙動2009

    • Author(s)
      柘植直樹
    • Organizer
      日本数学会特別講演
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] 大自由度大域結合写像系の間欠的挙動とその相転移2009

    • Author(s)
      茶碗谷毅
    • Organizer
      日本物理学会2009年秋季大会
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 秩序パラメータを最大化する振動子ネットワークの理論的考察2009

    • Author(s)
      茶碗谷毅、青柳富誌生
    • Organizer
      日本物理学会2009年秋季大会
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the stationary Navier-Stokes equations in a 3D bounded domain under the nonhomogeneous boundary condition2009

    • Author(s)
      柳沢卓
    • Organizer
      Conference on "Mathematical Physics and PDEs"
    • Place of Presentation
      Levico Terme (Trento), Italy
    • Year and Date
      2009-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] A remark on global weak solution in time for a system of compressible viscous fluid with large external potential force2009

    • Author(s)
      松村昭孝
    • Organizer
      共同研究集会「流体と気体の数学解析」
    • Place of Presentation
      数理解析研究所
    • Year and Date
      2009-07-09
    • Related Report
      2010 Final Research Report
  • [Presentation] A remark on global weak solution in time for a system of compressible viscous fluid with large external potential force2009

    • Author(s)
      松村昭孝
    • Organizer
      数理解析研究所共同研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-07-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Relaxation limits and asymptotic behaviors of solutions to the hydrodynamic model for semiconductors2008

    • Author(s)
      西畑伸也
    • Organizer
      12th Int. Conf. on Hyperbolic Problems
    • Place of Presentation
      University of Maryland, U.S.A
    • Year and Date
      2008-06-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Relaxation limits and asymptotic behaviors of solutions to the hydrodynamic model for semiconductors2008

    • Author(s)
      西畑伸也
    • Organizer
      12th Int. Conf. on Hyperbolic Problems
    • Place of Presentation
      University of Maryland, U.S.A.
    • Year and Date
      2008-06-13
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 一次元粘性保存則系の解の長時間挙動 I, II2007

    • Author(s)
      松村昭孝
    • Organizer
      研究集会「微分方程式の総合的研究」
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2007-12-14
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Heat-conductive hydrodynamic model for semiconductors: asymptotic behavior and relaxation limit2007

    • Author(s)
      Shinya Nishibata
    • Organizer
      International conference on conservation laws and kinetic equations
    • Place of Presentation
      Shanghai Jaotong University, Shanghai, China
    • Year and Date
      2007-11-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] 単独粘性保存則に対する半直線上のある初期値境界値問題について2007

    • Author(s)
      橋本伊都子、松村昭孝
    • Organizer
      日本数学会 秋期総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] 圧縮性オイラー方程式の球対称解について2007

    • Author(s)
      柘植直樹
    • Organizer
      発展方程式研究集会
    • Place of Presentation
      中央大学
    • Year and Date
      2007-09-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] Behavior of solutions to the Cauchy problem for the damped wave equation2007

    • Author(s)
      Kenji Nishihara
    • Organizer
      6-th ISAAC Congress
    • Place of Presentation
      Middle East Technical University, Ankara
    • Year and Date
      2007-08-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Decomposition theorems of vector fields and the application to the Navier-Stokes eauations2007

    • Author(s)
      Taku Yanagisawa
    • Organizer
      Second Workshop on Nonlinear Partial Differential Equations: Analysis, computation and Application
    • Place of Presentation
      Seoul National University, Korea
    • Year and Date
      2007-06-01
    • Related Report
      2007 Annual Research Report
  • [Presentation] 一次元粘性保存則系の解の長時間挙動I,II2007

    • Author(s)
      松村昭孝
    • Organizer
      研究集会「微分方程式の総合的研究」
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2010 Final Research Report
  • [Presentation] 一次元圧縮性粘性流体の長時間挙動

    • Author(s)
      松村昭孝
    • Organizer
      九州非線形偏微分方程式冬の学校
    • Place of Presentation
      九州大学箱崎キャンパス工学部本館
    • Related Report
      2008 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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