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 gasut+a⋅∇u2+divq=0,−∇divq+q+∇u=0, with initial datau(x1,…,xn,0)=u0(x1,…,xn)→u±,x1→±∞. First, for the case with the same end states u−=u+=0u−=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 LpLp-convergence rates of solutions are respectively obtained by applying L2L2-energy method for n=1,2,3n=1,2,3 and LpLp-energy method for 3