NONLOCAL FIRST-ORDER HAMILTON-JACOBI EQUATIONS MODELLING DISLOCATIONS DYNAMICS

Abstract : We study nonlocal first-order equations arising in the theory of dislocations. We prove the existence and uniqueness of the solutions of these equations in the case of positive and negative velocities, under suitable regularity assumptions on the initial data and the velocity. These results are based on new $L^1$-type estimates on the viscosity solutions of first-order Hamilton-Jacobi Equations appearing in the so-called level-sets approach''. Our work is inspired by and simplifies a recent work of Alvarez, Cardaliaguet and Monneau.
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https://hal.archives-ouvertes.fr/hal-00021694
Contributeur : Olivier Ley <>
Soumis le : vendredi 24 mars 2006 - 09:33:14
Dernière modification le : vendredi 16 novembre 2018 - 01:23:47
Document(s) archivé(s) le : samedi 3 avril 2010 - 21:10:45

Citation

Guy Barles, Olivier Ley. NONLOCAL FIRST-ORDER HAMILTON-JACOBI EQUATIONS MODELLING DISLOCATIONS DYNAMICS. Comm. Partial Differential Equations, 2006, 31 (7-9), pp.1191-1208. ⟨10.1080/03605300500361446⟩. ⟨hal-00021694⟩

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