Self-similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws

Here, we study the Riemann problem for a strictly hyperbolic system of conservation laws, which occurs in gas dynamics and nonlinear elasticity. We establish the existence and uniqueness of the solution of Riemann problem containing delta shock wave by employing self-similar vanishing viscosity approach. We prove that delta shock is stable under self-similar viscosity perturbation, which ensures that delta shock wave is a unique entropy solution.