Asymptotic behavior of solutions to a hyperbolic–elliptic coupled system in multi-dimensional radiating gas

This paper is concerned with the asymptotic behavior of solutions to the Cauchy problem of a hyperbolic–elliptic coupled system in the multi-dimensional radiating gas with initial data First, for the case with the same end states u−=u+=0, we prove the existence and uniqueness of the global solutions to the above Cauchy problem by combining some a priori estimates and the local existence based on the continuity argument. Then Lp-convergence rates of solutions are respectively obtained by applying L2-energy method for n=1,2,3 and Lp-energy method for 3