Nonlocal Hamilton-Jacobi equations related to dislocation dynamics and a FitzHugh-Nagumo systemReportar como inadecuado




Nonlocal Hamilton-Jacobi equations related to dislocation dynamics and a FitzHugh-Nagumo system - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 LMPT - Laboratoire de Mathématiques et Physique Théorique 2 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : We describe recent existence and uniqueness results obtained for nonlocal nonmonotone Eikonal equations modelling the evolution of interfaces. We focus on two model cases. The first one arises in dislocation dynamics and the second one comes from a FitzHugh-Nagumo system. The equation is nonlocal since, in both case, the velocity at a point of the boundary of the interface depends on the whole enclosed set via a convolution. In these models, the evolution is nonmonotone since we do not expect to have an inclusion principle.

Keywords : $L^1-$dependence in time Nonlocal Hamilton-Jacobi Equations dislocation dynamics Fitzhugh-Nagumo system nonlocal front propagation level-set approach lower-bound gradient estimate viscosity solutions eikonal equation $L^1-$dependence in time.





Autor: Olivier Ley -

Fuente: https://hal.archives-ouvertes.fr/



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