Weak Solutions for Dislocation Type Equations

Details Weak Solutions for Dislocation Type Equations Weak Solutions for Dislocation Type Equations

2008-02-07

arxiv.org/abs/0802.0931v1

International Conference for the 25th Anniversary of Viscosity Solutions, Tokyo : Japon (2007)

Mathematics

Analysis of PDEs

Scientific paper

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.

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