Asymptotic stability of viscous contact wave for the 1D radiation hydrodynamics system
Asymptotic stability of viscous contact wave for the 1D radiation hydrodynamics system
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DOI：
10.1016/j.jde.2011.03.011
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发表时间：
2011-08
影响因子：
2.4
通讯作者：
Jing Wang;Feng Xie
中科院分区：
文献类型：
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作者：
Jing Wang;Feng Xie
本文研究了辐射气体模型解的大时间行为，该模型在数学上表示为一维双曲-椭圆耦合系统的Cauchy问题，适当地给定远场状态。假设相应的欧拉方程组的黎曼问题存在接触间断波，那么我们可以构造出这样一个双曲椭圆方程组的粘性接触波。基于能量方法和辐射通量方程的椭圆性，我们证明了只要接触间断的强度和初始数据的扰动适当小，"粘性接触波"是渐近稳定的。
This paper is concerned with the large time behavior of solutions to a radiating gas model, which is represented mathematically as a Cauchy problem for a one-dimensional hyperbolic–elliptic coupled system, with suitably given far field states. Suppose the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, then we can construct a “viscous contact wave” for such a hyperbolic–elliptic system. Based on the energy methods and the ellipticity of the radiation flux equation, we prove that the “viscous contact wave” is asymptotically stable provided that the strength of contact discontinuity and the perturbation of the initial data are suitably small.