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

相变动力学守恒定律非严格双曲非线性偏微分方程组解的结构和奇异摄动极限

• 批准号: 18540202
• 负责人: YAMAZAKI Mitsuru
• 金额: $ 2.7万
• 依托单位: International Christian University (2007-2009)University of Tsukuba (2006)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540202/
• 关键词: 超局所解析; 偏微分方程式; 双曲型保存則系; エントロピー; 流体力学; 双曲型保存; 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; 双曲型保存則; 国際研究者交流(フランス); 国際研究者交流(韓国); 相対性理論; 特異摂動極限; オイラー方程

(1) We show that, for the 2×2 nonlinear hyperbolic systems of conservation laws with an umbilic point, there exists classical solutions, shock waves and also non-classical solutions, overcompressive shock waves. (2) We give a sufficient condition for guarantee that the singular perturbation limits of the hyperbolic conservation conservation equation with a higher order terms converge to the solution to the conservation law. (3) We prove the existence of solutions including vacuum to the relativistic Euler equation by using the compensated compactness method. (4) We show the stability of solution to the Boltzmann equation near vacuum in the context of general Lp spaces.

(1)证明了具有脐点的2×2非线性双曲型守恒律组存在经典解、超压激波和非经典解。(2)给出了带高阶项的双曲型守恒方程的奇摄动极限收敛于守恒律的解的充分条件。(3)利用补偿紧性方法证明了相对论欧拉方程解的存在性。(4)证明了一般Lp空间中Boltzmann方程在真空附近解的稳定性。

项目成果

Entropy solutions of the Euler equations for isothermal relativistic fluids

• DOI: 10.1504/ijdsde.2007.013742
• 发表时间: 2007-01
• 期刊: International Journal of Dynamical Systems and Differential Equations
• 影响因子: 0.3
• 作者: P. LeFloch;M. Yamazaki

Lp-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model

空间非均匀离散速度玻尔兹曼模型的 Lp 稳定性估计

• 发表时间: 2009
• 期刊: Discrete and Continuous Dynamical Systems-Series B 11
• 作者: Seung-Yeal Ha;Mitsuru Yamazaki
• 通讯作者: Mitsuru Yamazaki

Uniform Lp-stability theory for the spatially inhomogeneous Boltzmann equation near vacuum

近真空空间非齐次玻尔兹曼方程的均匀 Lp 稳定性理论

• 发表时间: 2008
• 期刊: Journal of Hyperbolic Differential Equations 5
• 作者: Seung-Yeal Ha;Mitsuru Yamazaki
• 通讯作者: Mitsuru Yamazaki

Vanishing at Most Seventh--Order Terms of Scalar Conservation Laws

至多七阶消失--标量守恒定律的阶项

• 发表时间: 2008
• 期刊: Hyperbolic Problems : Theory, Numerics, Applications. Proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Superieure, Lyon, July 17-21, 2006, Springer-Verlag
• 作者: Naoki Fuiino;Mitsuru Yamazaki
• 通讯作者: Mitsuru Yamazaki

A convergence result on the Burgers equation of conservation laws

守恒定律Burgers方程的收敛结果

• 期刊: Proceeding of the Tenth International Conference on Hyperbolic Problems : Theory, Numerics, Application, Osaka, 2004. (to appear)
• 作者: Naoki Fujino;Mitsuru Yamazaki
• 通讯作者: Mitsuru Yamazaki