多层结构下非线性方程组的粘性消失极限

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多层结构下非线性方程组的粘性消失极限
The Viscosity Vanishing Limit of Systems of Nonlinear Equations underMultiple Structures

DOI: 10.12677/AAM.2023.1210434, PDF, 下载: 163 浏览: 2,713
作者: 童林曦, 肖慧, 戴冰清, 李昂：上海师范大学数理学院，上海
关键词: 粘性激波层；匹配渐近展开；能量估计；Viscous Shock Layer； Matched Asymptotic Expansion； Energy Estimates

摘要: 本文研究多层结构下一维非线性粘性方程组的粘性消失极限问题，证明当两个不相互作用的激波满足摘条件时，粘性方程组的解与无粘方程组的解之间具有渐近等价性。该问题的证明使用了与粘性激波剖面稳定性理论相关的匹配渐近分析和能量估计。我们首先通过多尺度的匹配渐近展开方法构造粘性方程组的近似解，再通过能量估计的方法进行稳定性分析从而得出最终结论。

Abstract: In this thesis, we study the vanishing viscous limit of one-dimensional nonlinear viscous system with multi-layer structure. It is proved that when two non-interacting shock waves satisfy the entropy condition for the inviscid system, the asymptotic equivalence can be achieved between the solution of the viscous system and the solution of the inviscid system. This is proved based on matched asymptotic analysis and energy estimate related to the stability theory of viscous shock profile. First, the approximate solution of the viscosity system is constructed by the multi-scale matched asymptotic expansion method, and then the final conclusion is obtained by the stability analysis with the method of energy estimate.

文章引用：童林曦, 肖慧, 戴冰清, 李昂. 多层结构下非线性方程组的粘性消失极限[J]. 应用数学进展, 2023, 12(10): 4415-4436. https://doi.org/10.12677/AAM.2023.1210434

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