Open AccessPropagating fronts for a viscous Hamer-type system
Author(s) -
Giada Cianfarani Carnevale,
Corrado Lattanzio,
Corrado Mascia
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021130
Subject(s) - inviscid flow , mathematics , type (biology) , viscosity , mathematical physics , physics , mathematical analysis , mechanics , thermodynamics , ecology , biology
Motivated by radiation hydrodynamics, we analyse a \begin{document}$ 2\times2 $\end{document} 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 [ 21 ]. In addition, the case of small shocks and large viscosity is also addressed via a standard bifurcation argument.