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

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.
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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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