ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A MODEL SYSTEM OF RADIATING GAS WITH DISCONTINUOUS INITIAL DATA

Abstract

A one-dimensional model of radiating gas is obtained from approximating the system of radiating gas with thermo-nonequilibrium. The model system consists of a conservation law and a linear elliptic equation. In this paper, we study the global existence and the time asymptotic behavior of solutions to the model system with discontinuous initial data. Since the first equation is hyperbolic, the solutions contain discontinuities for any positive time. But, the uniqueness of solutions in weak sense holds by imposing the entropy condition. The main concern of this research is to investigate the behavior of the discontinuities contained in the solutions. It is proved that the set of discontinuous points consists of a certain C1-curve. This discrepancy of values at the discontinuities of the solutions is shown to decay to zero exponentially fast as time tends to infinity. This property is utilized in showing that the solutions approach the corresponding smooth traveling waves with the rate t-1/4 in the supremum norm.