Skip to Main content Skip to Navigation
Journal articles

GLOBAL EXISTENCE RESULTS AND UNIQUENESS FOR DISLOCATION EQUATIONS

Abstract : We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence and uniqueness of Lipschitz and local-in-time solutions were available in some particular cases. In this paper, we propose a definition of weak solutions for which we are able to prove the existence for all time. Then we discuss the uniqueness of such solutions in several situations, both in the monotone and non monotone case.
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00129352
Contributor : Olivier Ley <>
Submitted on : Friday, February 13, 2009 - 4:26:03 PM
Last modification on : Wednesday, April 1, 2020 - 1:57:17 AM
Document(s) archivé(s) le : Wednesday, September 22, 2010 - 11:40:25 AM

Files

bclm08-v2.pdf
Files produced by the author(s)

Identifiers

Citation

Guy Barles, Pierre Cardaliaguet, Olivier Ley, Regis Monneau. GLOBAL EXISTENCE RESULTS AND UNIQUENESS FOR DISLOCATION EQUATIONS. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2008, 40 (1), pp.44-69. ⟨10.1137/070682083⟩. ⟨hal-00129352v2⟩

Share

Metrics

Record views

784

Files downloads

469