Abstract :
We consider a one-dimensional radiation hydrodynamics model in the case of the
equilibrium diffusion approximation which is described by the compressible Navier–
Stokes system with the additional terms in the pressure and internal energy respectively,
which embody the effect of radiation. Under the physical growth conditions on the heat
conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy
problem with large initial data, where the initial density and velocity may have differing
constant states at infinity. Moreover, we show that if there is no vacuum in the initial
density, then, the vacuum and concentration of the density will never occur in any finite
time
