Weak Solutions for Dislocation Type Equations

Date
Authors
Ley, Olivier
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
Keywords
Mathematics - Analysis of PDEs, 49L25, 35F25, 35A05, 35D05, 35B50, 45G10
Citation
Collections