Global Existence Results and Uniqueness for Dislocation Equations

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dc.creatorBarles, Guy
dc.creatorCardaliaguet, Pierre
dc.creatorLey, Olivier
dc.creatorMonneau, Regis
dc.date2007-02-06
dc.date2009-02-13
dc.date.accessioned2026-07-07T12:41:04Z
dc.date.available2026-07-07T12:41:04Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/0702153
dc.identifierhttp://arxiv.org/abs/math/0702153
dc.identifierSIAM J. Math. Anal. 40, 1 (2008) 44-69
dc.identifierdoi:10.1137/070682083
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219646
dc.subjectAnalysis of PDEs
dc.subject49L25, 35F25, 35A05, 35D05, 35B50, 45G10
dc.titleGlobal Existence Results and Uniqueness for Dislocation Equations
dc.typetext

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