Asymptotic stability of scalar multi-D inviscid shock waves

Denis Serre (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

In several space dimensions, scalar shock waves between two constant states u ± are not necessarily planar. We describe them in detail. Then we prove their asymptotic stability, assuming that they are uniformly non-characteristic. Our result is conditional for a general flux, while unconditional for the multi-D Burgers equation.

Mots clés: Scalar conservation laws; Burgers equation; shock waves; contraction semigroup; asymptotic stability. MSC2010: 35L65; 35B40

Domaines: Equations aux dérivées partielles [math.AP]

Denis Serre. Asymptotic stability of scalar multi-D inviscid shock waves. 2021. ⟨ensl-03169397⟩