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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Article dans une revue
Comm. Partial Differential Equations, 2006, 31 (7-9), pp.1191-1208. <10.1080/03605300500361446>
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Soumis le : vendredi 24 mars 2006 - 09:33:14
Dernière modification le : mercredi 12 juillet 2017 - 01:15:32
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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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