Research of applied analysis toward the global theory for nonlinear systems

非线性系统全局理论的应用分析研究

• 批准号: 17340027
• 负责人: NISHIDA Takaaki
• 金额: $ 6.98万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17340027/
• 关键词: Nonlinear Partial Differential Equation; Dynamical Systems; Global structure of solution space; Heat convection problems; Computer assisted proof; Free surface problems; 非線形波動

Analysis for the heat convectin problems for the system of Oberbeck-Boussinesq equations in the horizontal strip domain. The existence of bifurcation curve of roll-type solutions is proved for the ten times Rayleigh number of critical Rayleigh number by a computer assisted proof . The second bifurcation point of stationary roll-type solutions is determined by a computer assisted proof. The hexagonal-type and rectangle-type solutions of 3-dimensional problems are also proved for the existence by a computer assisted proof at least for rather small Rayleigh numbers.The cocoon bifurcation for the Michelson system is analyzed and proved for the existence bf infinitely many bifurcations of heteroclinic orbits to the saddle-node periodic orbit by a topological method and a computer assisted proof.The driven-cavity problem of 2-dimensional Navier-Stokes equation is solved for rather large Reynolds numbers compared to the existing verified result by a Newton type computer assited proof.

水平条带域Oberbeck-Boussinesq方程组的热对流问题分析。通过计算机辅助证明，证明了临界瑞利数十倍瑞利数时滚型解分岔曲线的存在性。固定滚动型解的第二个分叉点由计算机辅助证明确定。 3维问题的六角型和矩形型解也通过计算机辅助证明至少对于相当小的瑞利数是存在的。分析并证明了迈克尔逊系统的茧分岔对于无穷多个的存在性。用拓扑方法和计算机辅助证明将异宿轨道分岔为鞍节点周期轨道。解决了二维纳维-斯托克斯方程的驱动腔问题与牛顿型计算机辅助证明的现有验证结果相比，对于相当大的雷诺数。

项目成果

Bifurcation problems of heat convection systems

热对流系统的分岔问题

• 发表时间: 2007
• 作者: Takaaki Nishida

Multi-clustered High Energy Solutions for a Phase Transition Problem

相变问题的多簇高能解决方案

• 发表时间: 2005
• 作者: K.Tanaka; P.Felmer; S.Martinez
• 通讯作者: S.Martinez

A unified theorem describing Hopf and pitchfork bifurcation

描述 Hopf 和干草叉分岔的统一定理

• 发表时间: 2006
• 作者: Tadashi Kawanago

Rigorous verfication of the cocoon bifurcation in the Michelson system

迈克尔逊系统中茧分岔的严格验证

• 发表时间: 2007
• 作者: H. kokubu; et. al.
• 通讯作者: et. al.

流体方程式系の解析・計算機援用解析

流体方程系统分析/计算机辅助分析

• 发表时间: 2005
• 作者: 西田 孝明