Partial Differential Equations
Global existence of solutions to a singular parabolic/Hamilton–Jacobi coupled system with Dirichlet conditions
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 945-950.

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.

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.

Received:
Published online:
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, Volume 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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