Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws

Abstract

In this article, we study the Riemann problem for a strictly hyperbolic system of conservation laws. The governing system arises in nonlinear elasticity and gas dynamics. The system is one of the examples of a strictly hyperbolic system whose Riemann solution consists of delta shock waves as well as classical elementary waves such as shock waves, rarefaction waves, and contact discontinuities. We discuss the existence and uniqueness of the solution of the Riemann problem involving δ-shock wave by using a self-similar vanishing viscosity approach. We show that δ-shock wave is a weak*-limit of L1 solution to some viscous perturbations as the viscosity vanishes.