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Global Existence Results and Uniqueness for Dislocation Equations

dc.contributor.authorBarles, Guy
HAL ID: 1242
dc.contributor.authorCardaliaguet, Pierre
dc.contributor.authorLey, Olivier
HAL ID: 2442
dc.contributor.authorMonneau, Régis
dc.date.accessioned2011-09-06T15:48:17Z
dc.date.available2011-09-06T15:48:17Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6931
dc.language.isoenen
dc.subjectnonlocal Hamilton–Jacobi equationsen
dc.subjectdislocation dynamicsen
dc.subjectnonlocal front propagationen
dc.subjectlevel-set approachen
dc.subjectgeometrical propertiesen
dc.subjectlower-bound gradient estimateen
dc.subjectviscosity solutionsen
dc.subjecteikonal equationen
dc.subjectL1-dependence in timeen
dc.subject.ddc515en
dc.titleGlobal Existence Results and Uniqueness for Dislocation Equationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe 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.en
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol40en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages44-69en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/070682083en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00129352/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelAnalyseen


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