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EnglishMotivated 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 [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.
| Titolo: | Propagating fronts for a viscous Hamer-type system | |
| Autori: | ||
| Data di pubblicazione: | 2022 | |
| Rivista: | ||
| Handle: | http://hdl.handle.net/11697/177073 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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