Motivated by radiation hydrodynamics, we analyse a 2 x 2 system consisting of a one-dimensional viscous conservation law with strictly convex flux -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 profile 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  and subsequently developed by Szmolyan . In addition, the case of small shocks and large viscosity is also addressed via a standard bifurcation argument.
|Titolo:||Propagating fronts for a viscous Hamer-type system|
|Data di pubblicazione:||2022|
|Appare nelle tipologie:||1.1 Articolo in rivista|