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

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dc.creatorIbrahim, H.
dc.creatorJazar, M.
dc.creatorMonneau, R.
dc.date2009-03-08
dc.date.accessioned2026-07-07T12:50:23Z
dc.date.available2026-07-07T12:50:23Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0903.1435
dc.identifierhttp://arxiv.org/abs/0903.1435
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222668
dc.subjectAnalysis of PDEs
dc.subject70H20; 49L25; 54C70; 46E30
dc.titleDynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system
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