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 R-n. When the initial perturbation corresponding to a positive constant state is sufficiently small in H-s(R-n). 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 L-p, 1 <= p <= + infinity, convergence rate of the solution. (C) 2008 Elsevier Ltd. All rights reserved.