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Communication Dans Un Congrès Année : 2009

Nonlocal Hamilton-Jacobi equations related to dislocation dynamics and a FitzHugh-Nagumo system

Résumé

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.
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Dates et versions

hal-00458216 , version 1 (19-02-2010)

Identifiants

  • HAL Id : hal-00458216 , version 1

Citer

Olivier Ley. Nonlocal Hamilton-Jacobi equations related to dislocation dynamics and a FitzHugh-Nagumo system. Viscosity solutions of differential equations and related topics, Jun 2008, Kyoto, Japan. pp.161-178. ⟨hal-00458216⟩
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