[Le problème de Dirichlet pour l'équation α-soliton de translation dans une bande]
Dans cette note, nous prouvons l'existence de solutions classiques au problème de Dirichlet pour l'équation de α-soliton de translation définie dans une bande de ; les données sur le bord sont deux copies d'une fonction convexe continue. Nous utilisons la méthode de Perron, dans laquelle une famille de grim reapers est employée comme barrière pour résoudre le problème de Dirichlet.
In this paper, we investigate the Dirichlet problem associated with the α-translating equation. Using the Perron method and a family of grim reapers as barriers, we prove the existence of a solution on a strip of and the boundary data is formed by two copies of a convex function.
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@article{CRMATH_2018__356_11-12_1179_0,
author = {Rafael L\'opez},
title = {The {Dirichlet} problem on a strip for the \protect\emph{\ensuremath{\alpha}}-translating soliton equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {1179--1187},
publisher = {Elsevier},
volume = {356},
number = {11-12},
year = {2018},
doi = {10.1016/j.crma.2018.10.005},
language = {en},
}
Rafael López. The Dirichlet problem on a strip for the α-translating soliton equation. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1179-1187. doi : 10.1016/j.crma.2018.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.10.005/
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