Global well-posedness and relaxation limits of a model for radiating gas

Abstract

We study the initial value problem for a hyperbolic–elliptic coupled system with arbitrary large discontinuous initial data. We prove existence and uniqueness for that model by means of L 1-contraction and comparison properties. Moreover, after suitable scalings, we study both the hyperbolic–parabolic and the hyperbolic–hyperbolic relaxation limits for that system.