Global Existence Results and Uniqueness for Dislocation Equations
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monneau, Régis (2008), Global Existence Results and Uniqueness for Dislocation Equations, SIAM Journal on Mathematical Analysis, 40, 1, p. 44-69. http://dx.doi.org/10.1137/070682083
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00129352/fr/Date
2008Journal name
SIAM Journal on Mathematical AnalysisVolume
40Number
1Publisher
SIAM
Pages
44-69
Publication identifier
Metadata
Show full item recordAbstract (EN)
We are interested in nonlocal eikonal equations arising in the study of the dynamics of dislocation lines in crystals. For these nonlocal but also nonmonotone 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 the nonmonotone case.Subjects / Keywords
nonlocal Hamilton–Jacobi equations; dislocation dynamics; nonlocal front propagation; level-set approach; geometrical properties; lower-bound gradient estimate; viscosity solutions; eikonal equation; L1-dependence in timeRelated items
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