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Dislocation dynamics with a mean curvature term: short time existence and uniqueness

Forcadel, Nicolas (2008), Dislocation dynamics with a mean curvature term: short time existence and uniqueness, Differential and Integral Equations, 21, 3-4, p. 285--304

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-00415911
Date
2008
Journal name
Differential and Integral Equations
Volume
21
Number
3-4
Publisher
American Mathematical Society
Pages
285--304
Metadata
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Author(s)
Forcadel, Nicolas cc
Abstract (EN)
In this paper, we study a new model for dislocation dynamics with a mean curvature term. The model is a non-local Hamilton-Jacobi equation. We prove a short time existence and uniqueness result for this equation. We also prove a Lipschitz estimate in space and an estimate of the the modulus of continuity in time for the solution.
Subjects / Keywords
viscosity solutions; Dislocation dynamics; non-local equations; mean curvature motion