Large-time asymptotic stability of Riemann shocks of scalar balance laws

Abstract

We prove the large-time asymptotic orbital stability of strictly entropic Riemann shock solutions of first order scalar hyperbolic balance laws, under piecewise regular perturbations provided that the source term is dissipative about endstates of the shock. Moreover the convergence towards a shifted reference state is exponential with a rate predicted by the linearized equations about constant endstates.