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Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system

Hassan Ibrahim 1, Mustapha Jazar 2, Régis Monneau 1

(25/05/2008)

We study a strongly coupled system of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied stress. The equations are written on a bounded interval and require special attention to the boundary layer. For this system, we prove a result of existence of a solution. The method of the proof consists in considering first a parabolic regularization of the full system, and then passing to the limit. For this regularized system, a result of global existence and uniqueness of a solution was given in a previous work of the authors. We show some uniform bounds on this solution which uses in particular an entropy estimate for the densities.

1 :	Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
	INRIA – Ecole des Ponts ParisTech
2 :	Mathematics Department
	Lebanese University

Domaine

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Mathématiques/Equations aux dérivées partielles

hal-00281859, version 1

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Contributeur : Hassan Ibrahim <>

Soumis le : Dimanche 25 Mai 2008, 15:49:51

Dernière modification le : Jeudi 29 Mai 2008, 21:12:08