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.
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Hassan Ibrahim 1; Mustapha Jazar 2; Régis Monneau 1
@article{CRMATH_2008__346_17-18_945_0,
author = {Hassan Ibrahim and Mustapha Jazar and R\'egis Monneau},
title = {Global existence of solutions to a singular {parabolic/Hamilton{\textendash}Jacobi} coupled system with {Dirichlet} conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {945--950},
publisher = {Elsevier},
volume = {346},
number = {17-18},
year = {2008},
doi = {10.1016/j.crma.2008.07.031},
language = {en},
}
TY - JOUR AU - Hassan Ibrahim AU - Mustapha Jazar AU - Régis Monneau TI - Global existence of solutions to a singular parabolic/Hamilton–Jacobi coupled system with Dirichlet conditions JO - Comptes Rendus. Mathématique PY - 2008 SP - 945 EP - 950 VL - 346 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2008.07.031 LA - en ID - CRMATH_2008__346_17-18_945_0 ER -
%0 Journal Article %A Hassan Ibrahim %A Mustapha Jazar %A Régis Monneau %T Global existence of solutions to a singular parabolic/Hamilton–Jacobi coupled system with Dirichlet conditions %J Comptes Rendus. Mathématique %D 2008 %P 945-950 %V 346 %N 17-18 %I Elsevier %R 10.1016/j.crma.2008.07.031 %G en %F CRMATH_2008__346_17-18_945_0
Hassan Ibrahim; Mustapha Jazar; Régis Monneau. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.031/
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