%0 Journal Article
%T Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system
%A H. Ibrahim
%A M. Jazar
%A R. Monneau
%J Mathematics
%D 2009
%I arXiv
%X We study a strongly coupled system consisting 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 with Dirichlet boundary conditions and require special attention to the boundary. We prove a result of global 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. We show some uniform bounds on this solution which uses in particular an entropy estimate for the densities.
%U http://arxiv.org/abs/0903.1435v1