## Shock waves for a model system of the radiating gas.(English)Zbl 0924.35082

This paper is concerned with the existence and asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. The authors show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of those traveling waves under the entropy condition, in the class of piecewise smooth functions which the first kind of discontinuities. Furthermore, they show that the $$c^3$$-smooth traveling waves are asymptotically stable and that the rate of convergence toward these waves is $$t^{-1/4}$$. In the proof of stability the energy method is used.

### MSC:

 35L67 Shocks and singularities for hyperbolic equations 35B35 Stability in context of PDEs 35Q35 PDEs in connection with fluid mechanics 76N15 Gas dynamics (general theory)
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