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

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.

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