Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system

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dc.creatorIbrahim, H.
dc.creatorJazar, M.
dc.creatorMonneau, R.
dc.date2009-03-05
dc.date.accessioned2026-07-07T12:49:18Z
dc.date.available2026-07-07T12:49:18Z
dc.descriptionWe study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the solution. Our system describes an approximate model of the dynamics of dislocation densities in a bounded channel submitted to an exterior applied stress. The system of equations is written on a bounded interval with Dirichlet conditions and requires a special attention to the boundary. The proof of existence and uniqueness is done under the use of two main tools: a certain comparison principle on the gradient of the solution, and a parabolic Kozono-Taniuchi inequality
dc.description36 pages
dc.identifierhttps://arxiv.org/abs/0903.0964
dc.identifierhttp://arxiv.org/abs/0903.0964
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222357
dc.subjectAnalysis of PDEs
dc.subject35K50; 35K40; 35K55; 42B35; 42B99
dc.titleDynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system
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