Development of study of nonlinear system as applied analysis

非线性系统应用分析研究的发展

• 批准号: 20540141
• 负责人: NISHIDA Takaaki
• 金额: $ 2.91万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540141/
• 关键词: 応用数学; 非線形偏微分方程式系; 力学系; 熱対流問題、; パターン形成; 解空間大域構造; 計算機援用解析; 計算機援用証明法; 熱対流問題

Main objects are Dynamical Systems, Nonlinear Hyperbolic Conservation Laws and Fluid Dynamical Equations. After considering the pattern formations and the structure of solutions we proceed to study their global structure of the solution spaces such as bifurcation diagrams and their stability by analysis and computer assisted analysis. Global bifurcation diagrams for Rayleigh-Benard heat convection problems, bifurcation theorems for Benard-Marangoni heat convection problems and a constructive existence theorem by a finite difference method for the Hamilton-Jacobi equation corresponding to a special Hamiltonian with two degree of freedom are obtained.

主要研究对象为动力系统、非线性双曲守恒律和流体动力方程。在考虑图案形成和结构的解决方案，我们着手研究其整体结构的解空间，如分歧图和他们的稳定性分析和计算机辅助分析。得到了Rayleigh-Benard热对流问题的全局分支图、Benard-Marangoni热对流问题的分支定理以及对应于一个特殊的两自由度Hamilton算子的Hamilton-Jacobi方程的构造性存在定理.

项目成果

Heat convection problems of compressible fluids, International Conference on Nonlinear Partial Differential Equations : Mathematical Theory, Computation, and Applications

可压缩流体的热对流问题，非线性偏微分方程国际会议：数学理论、计算和应用

• 发表时间: 2010
• 作者: Y. Yoshida;T. Maruta;西田孝明;Makoto Mori;只木孝太郎;Makoto Mori;A. Kikui. T. Maruta;西田孝明;Makoto Mori;只木孝太郎;T.Nishida
• 通讯作者: T.Nishida

Periodic solutions of the forced Burgers equation

受迫 Burgers 方程的周期解

• 发表时间: 2009
• 期刊: RIMS Kokyuroku 1631
• 作者: Takaaki Nishida;Kohei Soga
• 通讯作者: Kohei Soga

Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems

非线性热对流问题分叉解的计算机辅助证明

• 发表时间: 2010
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: M. Nakao;Yoshitaka Watanabe;N. Yamamoto;T. Nishida;Myoungnyoun Kim
• 通讯作者: Myoungnyoun Kim

Heat convection problems of compressible fluids

可压缩流体的热对流问题

• 发表时间: 2010
• 作者: Y. Yoshida;T. Maruta;西田孝明
• 通讯作者: 西田孝明

Pattern Formations in Heat Convection Problems, International Conference on Contemporary Applied Mathematics

热对流问题中的模式形成，当代应用数学国际会议

• 发表时间: 2009
• 作者: T.Nishida;Y.Teramoto;森真;Makoto Mori;T.Nishida
• 通讯作者: T.Nishida