Differential and Integral Equations

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

Nicolas Forcadel

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Abstract

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 modulus of continuity in time for the solution.

Article information

Source
Differential Integral Equations, Volume 21, Number 3-4 (2008), 285-304.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038781

Mathematical Reviews number (MathSciNet)
MR2484010

Zentralblatt MATH identifier
1224.49038

Subjects
Primary: 35G25: Initial value problems for nonlinear higher-order equations
Secondary: 35D05 35D10 49L25: Viscosity solutions 74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials) 74H20: Existence of solutions

Citation

Forcadel, Nicolas. Dislocation dynamics with a mean curvature term: short time existence and uniqueness. Differential Integral Equations 21 (2008), no. 3-4, 285--304. https://projecteuclid.org/euclid.die/1356038781


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