Weak Solutions for Dislocation Type Equations
Analysis of PDEs
2009-02-13 v1
Abstract
We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author recently. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations are nonlocal but also non monotone. We use a notion of weak solution to provide solutions for all time. Then, we discuss the link between these weak solutions and the classical viscosity solutions, and state some uniqueness results in particular cases. A counter-example to uniqueness is given.
Cite
@article{arxiv.0802.0931,
title = {Weak Solutions for Dislocation Type Equations},
author = {Olivier Ley},
journal= {arXiv preprint arXiv:0802.0931},
year = {2009}
}