Geodesic
Existence and uniqueness for dislocation dynamics with nonnegative velocity
Olivier Alvarez1 ; Pierre Cardaliaguet2 ; Régis Monneau3
1Université de Rouen, Mont-Saint-Aignan, France
2Université de Bretagne Occidentale, Brest, France
3CERMICS, Ecole nationale des Ponts et Chausées, Marne-La-Vallée, France
Interfaces and free boundaries, Tome 7 (2005) no. 4, pp. 415-434

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DOI

We study the problem of large time existence of solutions for a mathematical model describing dislocation dynamics in crystals. The mathematical model is a geometric and non local eikonal equation which does not preserve the inclusion. Under the assumption that the dislocation line is expanding, we prove existence and uniqueness of the solution in the framework of discontinuous viscosity solutions. We also show that this solution satisfies some variational properties, which allows to prove that the energy associated to the dislocation dynamics is non increasing.
DOI : 10.4171/ifb/131
Classification : 35-XX, 76-XX, 37-XX, 00-XX
Mots-clés : Dislocation dynamics, eikonal equation, Hamilton-Jacobi equations, discontinuous viscosity solutions, non-local equations

Olivier Alvarez  1   ; Pierre Cardaliaguet  2   ; Régis Monneau  3

1 Université de Rouen, Mont-Saint-Aignan, France
2 Université de Bretagne Occidentale, Brest, France
3 CERMICS, Ecole nationale des Ponts et Chausées, Marne-La-Vallée, France 
Olivier Alvarez; Pierre Cardaliaguet; Régis Monneau. Existence and uniqueness for dislocation dynamics with nonnegative velocity. Interfaces and free boundaries, Tome 7 (2005) no. 4, pp. 415-434. doi: 10.4171/ifb/131
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     title = {Existence and uniqueness for dislocation dynamics with nonnegative velocity},
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     pages = {415--434},
     year = {2005},
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     number = {4},
     doi = {10.4171/ifb/131},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/131/}
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