Coupling techniques for nonlinear hyperbolic equations

Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch

January 2014

Résumé

We analyze the coupling between different nonlinear hyperbolic equations across possibly resonant interfaces. The proposed reformulation of the problem involves a nonconservative product that is understood through a self-similar viscous approximation. We obtain the existence of a coupled solution to the Riemann problem in this thin interface regime, and underline the persisting multiplicity of solutions for some Riemann data, even in simple situations. Another regularization strategy is then studied, that corresponds somehow to a thick interface regime. This other selection criterion leads to a well-posed problem and we thus consider a finite volume scheme to approximate its solution.