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arXiv · 0903.1435

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

H. Ibrahim·M. Jazar·R. Monneau
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Abstract

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.

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H. Ibrahim, M. Jazar, R. Monneau. 2009-03-08. Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system. https://arxiv.org/abs/0903.1435

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