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

摘要

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. u_t+a·▽u~2+divq=0,-▽divq+q+▽u=0, with initial data. u(x_1,...,x_n,0)=u0(x_1,...,x_n)→u±,x_1→±∞. 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 L~p-convergence rates of solutions are respectively obtained by applying L~2-energy method for n=1,2,3 and L~p-energy method for 3