Asymptotic analysis for systems of a hyperbolicparabolic type appeared in fluid dynamics

流体动力学中出现双曲抛物型系统的渐近分析

• 批准号: 21740100
• 负责人: NAKAMURA Tohru
• 金额: $ 2.58万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740100/
• 关键词: 解析学; 偏微分方程式論; 流体力学; 圧縮性流体; 漸近解析; エネルギー法; 粘性保存則; 境界層解; 漸近挙動

In the present research, we consider an existence and an asymptotic stability of a boundary layer solution(stationary wave) for model systems of compressible and viscous gases. More precisely, we prove the existence and the asymptotic stability of boundary layer solution for an outflow and an inflow problems of heatconductive model. Moreover, we show the existence of boundary layer solution for model systems of symmetric hyperbolicparabolic type.

在本研究中，我们考虑可压缩粘性气体模型系统边界层解（驻波）的存在性和渐近稳定性。更精确地，我们证明了热传导模型的流出和流入问题的边界层解的存在性和渐近稳定性。此外，我们还证明了对称双曲抛物型模型系统边界层解的存在性。

项目成果

Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate

• DOI: 10.1142/s0218202510004908
• 发表时间: 2009-12
• 期刊: Mathematical Models and Methods in Applied Sciences
• 影响因子: 3.5
• 作者: S. Kawashima;Tohru Nakamura;S. Nishibata;P. Zhu

Energy method in the partial Fourier space and application to stability problems in the half space.

部分傅里叶空间中的能量方法及其在半空间稳定性问题中的应用。

• DOI: 10.1016/j.jde.2010.10.003
• 发表时间: 2011
• 期刊: J. Differential Equations
• 作者: Y. Ueda;T. Nakamura;S. Kawashima
• 通讯作者: S. Kawashima

STATIONARY WAVE ASSOCIATED WITH AN INFLOW PROBLEM IN THE HALF LINE FOR VISCOUS HEAT-CONDUCTIVE GAS

• DOI: 10.1142/s0219891611002524
• 发表时间: 2011-12
• 期刊: Journal of Hyperbolic Differential Equations
• 影响因子: 0.7
• 作者: Tohru Nakamura;S. Nishibata