Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves

In this paper we consider a hyperbolic-hyperbolic relaxation limit problem for a 1D compressible radiation hydrodynamics (RHD) system. The RHD system consists of the full Euler system coupled with an elliptic equation for the radiation flux. The singular relaxation limit process we consider corresponds to the physical problem of letting the Bouguer number become infinite. We prove for appropriate initial datum that the solution of the initial …