Partial Differential Equations
Global existence of solutions to a singular parabolic/Hamilton–Jacobi coupled system with Dirichlet conditions
[Existence globale de solutions pour un système couplé parabolique/Hamilton–Jacobi singulier avec condition de Dirichlet]
Comptes Rendus. Mathématique, Tome 346 (2008) no. 17-18, pp. 945-950.

Nous étudions l'existence de solutions mixtes (distribution/viscosité) pour un système couplé parabolique/Hamilton–Jacobi posé sur un interval. Notre motivation vient de l'étude de la dynamique de densités de dislocations dans un cristal de taille finie. L'idée de la preuve consiste à considérer une régularisation parabolique appropriée, et ensuite à passer à la limite en utilisant en particulier une estimation entropique pour les densités.

We study the existence of (distribution/viscosity) solutions of a singular parabolic/Hamilton–Jacobi coupled system. Our motivation stems from the study of the dynamics of dislocation densities in a crystal of finite size. The method of the proof consists in considering a parabolic regularization of the system, and then passing to the limit after obtaining some uniform bounds using in particular an entropy estimate for the densities.

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Publié le :
DOI : 10.1016/j.crma.2008.07.031
Ibrahim, Hassan 1 ; Jazar, Mustapha 2 ; Monneau, Régis 1

1 CERMICS, École des ponts, Université Paris-Est, 6 & 8, avenue B. Pascal, 77455 Marne-la-Vallée cedex 2, France
2 LaMA-Liban, Lebanese University, P.O. Box 826, Tripoli, Lebanon
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Ibrahim, Hassan; Jazar, Mustapha; Monneau, Régis. Global existence of solutions to a singular parabolic/Hamilton–Jacobi coupled system with Dirichlet conditions. Comptes Rendus. Mathématique, Tome 346 (2008) no. 17-18, pp. 945-950. doi : 10.1016/j.crma.2008.07.031. http://www.numdam.org/articles/10.1016/j.crma.2008.07.031/

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