Propagating fronts for a viscous Hamer-type system

Motivated by radiation hydrodynamics, we analyse a 2   2 system consisting of a one-dimensional viscous conservation law with strictly convex ux -the viscous Burgers' equation being a paradigmatic example- coupled with an elliptic equation, named viscous Hamer-type system. In the regime of small viscosity and for large shocks, namely when the pro le of the corresponding underlying inviscid model undergoes a discontinuity {usually called sub-shock{ it is proved the existence of a smooth propagating front, regularising the jump of the corresponding inviscid equation. The proof is based on Geometric Singular Perturbation Theory (GSPT) as introduced in the pioneering work of Fenichel [5] and subsequently developed by Szmolyan [21]. In addition, the case of small shocks and large viscosity is also addressed via a standard bifurcation argument.