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 [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.
Propagating fronts for a viscous Hamer-type system
Carnevale, Giada Cianfarani;Lattanzio, Corrado;
2022
Abstract
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 [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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
