Abstract
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 ≤ + ∞ , convergence rate of the solution.
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