The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions

In this paper, we study the time-asymptotic behavior of solutions for a hyperbolic–elliptic coupled system known as a model system of the radiating gas in RnRn. When the initial perturbation corresponding to a positive constant state is sufficiently small in Hs(Rn)Hs(Rn), the global existence and pointwise estimates of the solution are obtained by using the method of the Green function combined with some energy estimates. Furthermore, we obtain the LpLp, 1≤p≤+∞1≤p≤+∞, convergence rate of the solution.