[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 = {L\'opez, Rafael},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.10.005/}
}
TY - JOUR AU - López, Rafael TI - The Dirichlet problem on a strip for the α-translating soliton equation JO - Comptes Rendus. Mathématique PY - 2018 SP - 1179 EP - 1187 VL - 356 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.10.005/ DO - 10.1016/j.crma.2018.10.005 LA - en ID - CRMATH_2018__356_11-12_1179_0 ER -
%0 Journal Article %A López, Rafael %T The Dirichlet problem on a strip for the α-translating soliton equation %J Comptes Rendus. Mathématique %D 2018 %P 1179-1187 %V 356 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.10.005/ %R 10.1016/j.crma.2018.10.005 %G en %F CRMATH_2018__356_11-12_1179_0
López, Rafael. The Dirichlet problem on a strip for the α-translating soliton equation. Comptes Rendus. Mathématique, Tome 356 (2018) no. 11-12, pp. 1179-1187. doi : 10.1016/j.crma.2018.10.005. http://www.numdam.org/articles/10.1016/j.crma.2018.10.005/
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