Asymptotic stability of scalar multi-D inviscid shock waves

Authors :: Serre, Denis
Unité de Mathématiques Pures et Appliquées (UMPA-ENSL)
École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)
École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
Source :: Annales de l'Institut Fourier. :1-20
Publication Year :: 2023
Publisher :: Cellule MathDoc/CEDRAM, 2023.
Abstract: In several space dimensions, scalar shock waves between two constant states u $\pm$ 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.