Propagating Fronts for a Viscous Hamer-Type system
Abstract
Motivated by radiation hydrodynamics, we analyse a 2x2 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 [5] and subsequently developed by Szmolyan [19]. In addition, the case of small shocks and large viscosity is also addressed via a standard bifurcation argument.
Cite
@article{arxiv.2102.08033,
title = {Propagating Fronts for a Viscous Hamer-Type system},
author = {Giada Cianfarani Carnevale and Corrado Lattanzio and Corrado Mascia},
journal= {arXiv preprint arXiv:2102.08033},
year = {2021}
}