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

Vincent Duchêne (1, 2) , Luis Miguel Miguel Rodrigues (1, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 CNRS - Centre National de la Recherche Scientifique
3 IUF - Institut universitaire de France

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.

Mots clés: asymptotic stability; scalar balance laws; Riemann shocks

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Duchêne, Luis Miguel Miguel Rodrigues. Large-time asymptotic stability of Riemann shocks of scalar balance laws. SIAM Journal on Mathematical Analysis, 2020, 52 (1), ⟨10.1137/18M1221795⟩. ⟨hal-01898903v1⟩