Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics

Abstract

The governing equations in radiation hydrodynamics are derived from the conservation laws for macroscopic quantities, which have to be coupled with a radiative transfer equationto account for the radiative effects. In the present paper, we work with a mathematical model forthe diffusion approximation of radiation hydrodynamics in the simplified framework of 1-D flows.We prove the existence, uniqueness and regularity of global solutions to an initial-boundary valueproblem with large data. The existence of global solution is proved by combining the local existence theorem with the global a priori estimates, which are considerably complicated and somenew ideas and techniques are thus required. Moreover, it is shown that neither shock wavesnor vacuum and concentration in the solution are developed in a finite time although there is acomplex interaction between photons and matter.