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Coupling techniques for nonlinear hyperbolic equations. I: Self-similar diffusion for thin interfaces. (English) Zbl 1252.35188

The authors study coupling techniques for nonlinear hyperbolic systems in the setting of self-similar vanishing viscosity approximations to the Riemann problem for general hyperbolic systems. They introduce an augmented formulation that allows for the modeling of the dynamics of interfaces between fluid flows. An existence result for the Riemann problem is given under general assumptions on the nonlinear hyperbolic system and its regularization. Nonlinear wave interaction estimates for solutions which apply in the resonant case where global hyperbolicity is lost are obtained.

MSC:

35L60 First-order nonlinear hyperbolic equations
35L45 Initial value problems for first-order hyperbolic systems
35D30 Weak solutions to PDEs
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