Shock waves for a model system of the radiating gas
Shock waves for a model system of the radiating gas
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DOI：
10.1137/s0036141097322169
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发表时间：
1999
影响因子：
2
通讯作者：
S. Kawashima;S. Nishibata
中科院分区：
文献类型：
--
作者：
S. Kawashima;S. Nishibata
本文关注的是通过近似辐射气体一维系统导出的模型系统行波的存在性和渐近稳定性。我们证明了光滑或不连续行波的存在性，并证明了这些行波在熵条件下，在具有第一类不连续性的分段光滑函数类中的唯一性。此外，我们表明 C3 平滑行波是渐近稳定的，并且这些波的收敛率为 t-1/4 ，这看起来是最佳的。通过将标准能量法应用于原方程的积分方程，给出了稳定性证明。
This paper is concerned with the existence and the asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. We show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of these traveling waves under the entropy condition, in the class of piecewise smooth functions with the first kind discontinuities. Furthermore, we show that the C3 -smooth traveling waves areasymptotically stable and that the rate of convergence toward these waves is t-1/4 , which looks optimal. The proof of stability is given by applying the standard energy method to the integrated equation of the original one.