Asymptotic stability of scalar multi-D inviscid shock waves
Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 2079-2098.

In several space dimensions, scalar shock waves between two constant states are not necessarily planar. We describe them in detail. Then we prove their asymptotic stability in L 1 -distance, assuming that they are uniformly non-characteristic. Our result is conditional for a general flux, while unconditional for the multi-D Burgers equation.

En plusieurs variables d’espace, les chocs scalaires entre deux constantes u ± ne sont pas nécessairement des chocs plans. Nous les décrivons en détail. Puis nous prouvons leur stabilité asymptotique en distance L 1 , sous l’hypothèse qu’ils ne sont pas caractéristiques. Pour un flux général, notre résultat suppose que la donée initiale est à valeurs dans l’intervalle [u + ,u - ]. Pour l’équation de Burgers multi-D, il est valable pour des perturbations arbitrairement grandes.

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Accepted:
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DOI: 10.5802/aif.3569
Classification: 35L65, 35B40
Keywords: Scalar conservation laws, Burgers equation, shock waves, contraction semi-group, asymptotic stability.
Mot clés : Lois de conservation scalaires, équation de Burgers, ondes de choc, semi-groupe de contractions, stabilité asymptotique.
Serre, Denis 1

1 U.M.P.A., UMR 5669, CNRS–ENSL ENS de Lyon, 46 allée d’Italie 69364 Lyon cedex 07 (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Serre, Denis. Asymptotic stability of scalar multi-D inviscid shock waves. Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 2079-2098. doi : 10.5802/aif.3569. https://aif.centre-mersenne.org/articles/10.5802/aif.3569/

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