2021/02/16 by Giada Cianfarani Carnevale, Carnevale, Giada Cianfarani, Corrado Lattanzio +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.2102.08033
arxiv created 2021/02/16 · arxiv updated 2021/02/17
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.