Structures and singular perturbations limits of solutions to the systems of non-strictly hyperbolic nonlinear partial differential equations for the conservation laws in the phase transition dynamics

2008 Fiscal Year Self-evaluation Report

• Project/Area Number: 18540202
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: International Christian University (2007-2009); University of Tsukuba (2006)
• Principal Investigator: YAMAZAKI Mitsuru International Christian University, 教養学部, 教授 (30240732)
• Project Period (FY): 2006 – 2009
• Keywords: 超局所解析 / 流体力学 / 双曲型保存則 / 特殊相対論 / オイラー方程式 / ボルツマン方程式 / 多重双曲型 / エントロピー

Research Abstract

この研究の主目的は、相対論的オイラー方程式、ボルツマン方程式およびその拡張された速度離散モデル、1点で強双曲性が退化している非線形双曲型保存則系、単独保存則系の特異摂動極限を調べることにあるが、最終目的は、より広範囲の流体力学の方程式および非線形双曲型保存則系の解の構造を解明することにある。

Research Products

• [Journal Article] Lp-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model (2009)
  • Author(s): Seung-Yeal Ha, Mitsuru Yamazaki
  • Journal Title: Discrete and Continuous Dynamical Systems - Series B 11 Pages: 353-364
  • Peer Reviewed
• [Journal Article] Uniform Lp-stability theory for the spatially inhomogeneous Boltzmann equation near vacuum (2008)
  • Author(s): Seung-Yeal Ha, Mitsuru Yamazaki
  • Journal Title: Journal of Hyperbolic Differential Equations 5 Pages: 713-739
  • Peer Reviewed
• [Journal Article] Burgers' type equation with vanishing higher order (2007)
  • Author(s): Naoki Fujino, Mitsuru Yamazaki
  • Journal Title: Commun. Pur. Appl. Anal 6 Pages: 505-520
  • Peer Reviewed
• [Journal Article] Entropy solutions of the Euler equations for isothermal relativistic fluids (2007)
  • Author(s): Philippe G. LeFloch, Mitsuru Yamazaki
  • Journal Title: International Journal of Dynamical Systems and Differential Equations 1 Pages: 20-37
  • Peer Reviewed
• [Journal Article] Hyperbolic conservation laws with nonlinear diffusion and nonlinear dispersion (2006)
  • Author(s): Naoki Fujino, Mitsuru Yamazaki
  • Journal Title: Journal of Differential Equations 228 Pages: 171-190
  • Peer Reviewed
• [Presentation] Introduction to the theory on compensated compactness (2008)
  • Author(s): Mitsuru Yamazaki
  • Organizer: HYKE (HYperbolic and KinEtic) Seminar, Department of Mathematical Sciences
  • Place of Presentation: Seoul National University, Seoul, Korea
  • Year and Date: 20081100
• [Presentation] 特殊相対論における等温流体のダイナミックス (2007)
  • Author(s): Mitsuru Yamazaki
  • Organizer: 日本数学会2007年度秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 20070900
• [Presentation] "ボルツマン方程式の解の一様Lp-安定性", OS2-2 自己相互作用流体の平衡状態とその安定性 (2007)
  • Author(s): Mitsuru Yamazaki
  • Organizer: 第56回理論応用力学講演会
  • Place of Presentation: 日本学術会議
  • Year and Date: 20070300
• [Presentation] Scalar conservation laws with nonlinear diffusion and nonlinear dispersion (2006)
  • Author(s): Mitsuru Yamazaki
  • Organizer: 11^<th> International Conference on Hyperbolic Problems Theory, Numerics, Applications, Ecole Normale Superieure de Lyon
  • Place of Presentation: Lyon, France
  • Year and Date: 20060700
• [Presentation] The dynamics of isothermal relativistic fluids (2006)
  • Author(s): Mitsuru Yamazaki
  • Organizer: 超関数と線型微分方程式2006
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20060300