Weak Solutions for Dislocation Type Equations
نویسنده
چکیده
We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author in [9, 7]. 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. —————————————————————————— Communicated by xxxxxxxxxxxx; Received xxxxxxxxxx, 2007. This work is supported by xxxxxxxxxxxxxxxxxxxx.
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