# American Institute of Mathematical Sciences

July  2015, 35(7): 3015-3037. doi: 10.3934/dcds.2015.35.3015

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

 1 Department of Mathematics, College of Science, Hohai University, Nanjing 210098, China

Received  October 2013 Revised  March 2014 Published  January 2015

The governing equations in radiation hydrodynamics are derived from the conservation laws for macroscopic quantities, which have to be coupled with a radiative transfer equation to account for the radiative effects. In the present paper, we work with a mathematical model for the 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 value problem 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 some new ideas and techniques are thus required. Moreover, it is shown that neither shock waves nor vacuum and concentration in the solution are developed in a finite time although there is a complex interaction between photons and matter.
Citation: Peng Jiang. Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete & Continuous Dynamical Systems, 2015, 35 (7) : 3015-3037. doi: 10.3934/dcds.2015.35.3015
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