no. 5
Asymptotic stability of scalar multi-D inviscid shock waves
[Stabilité asymptotique des chocs scalaires non visqueux en plusieurs variables d’espace]
Serre, Denis1
1 U.M.P.A., UMR 5669, CNRS–ENSL ENS de Lyon, 46 allée d’Italie 69364 Lyon cedex 07 (France)
Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 2079-2098.

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.

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.

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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)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Asymptotic stability of scalar {multi-D} inviscid shock waves},
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Serre, Denis. Asymptotic stability of scalar multi-D inviscid shock waves. Annales de l'Institut Fourier, Tome 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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