Toward a Global Analysis for Nonlinear System of Partial Differential Equations

非线性偏微分方程组的全局分析

• 批准号: 23540253
• 负责人: NISHIDA Takaaki
• 金额: $ 3.08万
• 依托单位: Kyoto University (2012-2013)Waseda University (2011)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540253/
• 关键词: 大域的解析; 非線形偏微分方程式; 力学系; 熱対流問題; 圧縮性粘性熱伝導性流体; Jauslin-Kreiss-Moser モデル; 計算機援用解析; 非線形偏微分方程式系

Heat convection problems of compressible, viscous and heat-conductive fluids are investigated. Stationary bifurcations are proved to occur from the equilibrium state ( heat conduction solution ), when the Rayleigh number exceeds the critical value. They correspond to the pattern formation of the roll-type solution, the hexagonal cell and the mixed type solution. The bifurcation occurs uniformly with respect to the parameter which corresponds to the gradient of temperature and they converge to those of the Oberbeck-Boussinesq equation as the parameter tends to zero.Jauslin-Kreiss-Moser model of Hamilton Mechanics is investigated. It is a periodically forced Burgers equation with the periodic boundary condition.The periodic in time solutions are constructed by the Lax-Friedrichs scheme and the periodic, chaotic solutions and the Aubry-Mather set are obtained numerically.

研究了可压缩、粘性、导热流体的对流换热问题。稳态分岔被证明发生从平衡状态（热传导解决方案），当瑞利数超过临界值。它们对应于卷型溶液、六角胞和混合型溶液的图案形成。当温度梯度参数趋于零时，分岔点一致收敛于Oberbeck-Boussinesq方程的分岔点。研究了汉密尔顿力学的Jauslin-Kreiss-Moser模型。这是一个具有周期边界条件的周期受迫Burgers方程，利用Lax-Friedrichs方法构造了该方程的周期时间解，并数值计算了该方程的周期解、混沌解和Aubry-Mather集.

项目成果

Heat convection problems of compressible viscous fluids

可压缩粘性流体的热对流问题

• 发表时间: 2013
• 作者: 舘内謙;本原顕太郎;小西真広;高橋英則;他;Takaaki Nishida
• 通讯作者: Takaaki Nishida

Difference approximation to Aubry–Mather sets of the forced Burgers equation

强制 Burgers 方程的 AubryâMather 集的差分近似

• DOI: 10.1088/0951-7715/25/9/2401
• 发表时间: 2012
• 期刊: Nonlinearity
• 影响因子: 1.7
• 作者: T. Nishida;K. Soga
• 通讯作者: K. Soga

Heat convection of compressible viscous fluids. I

可压缩粘性流体的热对流。

• DOI: 10.1007/s00021-012-0112-3
• 发表时间: 2012
• 期刊: Journal of Mathematical Fluid Mechanics
• 影响因子: 1.3
• 作者: Takaaki Nishida;Mariarosaria Padula and Yoshiaki Teramoto
• 通讯作者: Mariarosaria Padula and Yoshiaki Teramoto

Hyperbolic conservation laws without the convexity

无凸性的双曲守恒定律

• 发表时间: 2011
• 作者: Nomoto;K.;Kobayashi;C.;Tominaga;N.;Takaaki Nishida
• 通讯作者: Takaaki Nishida

Heat Convection of Compressible Viscous Fluids. II

• DOI: 10.1007/s00021-013-0139-0
• 发表时间: 2013-04
• 期刊: Journal of Mathematical Fluid Mechanics
• 影响因子: 1.3
• 作者: T. Nishida;M. Padula;Yoshiaki Teramoto