A Gas-Solid Free Boundary Problem for a Compressible Viscous Gas

A Gas-Solid Free Boundary Problem for a Compressible Viscous Gas
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DOI：
10.1137/s0036141002403730
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发表时间：
2003
期刊：
SIAM J. Math. Anal.
影响因子：
--
通讯作者：
F. Huang;A. Matsumura;Xiaoding Shi
F. Huang;A. Matsumura;Xiaoding Shi
中科院分区：
其他
文献类型：
--
作者：
F. Huang;A. Matsumura;Xiaoding Shi

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本文提出了与流入问题相关的可压缩粘性气体一维模型系统的气固自由边界问题，其中固体不断变成气体并在自由边界上产生气体的流入。首先证明了行波解的存在性及其渐近稳定性。我们进一步讨论了行波解和稀疏波的组合给出解的渐近状态的情况。
In this paper we propose a gas-solid free boundary problem for a one-dimensional model system of a compressible viscous gas associated with the inflow problem, where the solid constantly changes into the gas and produces the inflow of the gas on the free boundary. We first show the existence of the traveling wave solution and its asymptotic stability. We further discuss the case in which the asymptotic state of the solution is given by a combination of the traveling wave solution and rarefaction wave.