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- W1978974498 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. Our system is a natural extension of that studied in [16 Ibrahim , H. ( 2009 ). Existence and uniqueness for a non-linear parabolic/Hamilton–Jacobi coupled system describing the dynamics of dislocation densities . Ann. Inst. H. Poincaré Anal. Non Linéaire 26 : 415 – 435 .[Crossref] , [Google Scholar]] where the applied stress was set to be zero. 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. For this regularized system, a result of global existence and uniqueness of a solution has been given in [17 Ibrahim , H. , Jazar , M. , Monneau , R. Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system. Preprint . [Google Scholar]]. We show some uniform bounds on this solution which uses in particular an entropy estimate for the densities." @default.
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- W1978974498 date "2009-07-27" @default.
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- W1978974498 title "Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System" @default.
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- W1978974498 doi "https://doi.org/10.1080/03605300903011861" @default.
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