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dc.contributor.authorMellet, Antoine
dc.contributor.authorImbert, Cyril
dc.date.accessioned2010-04-07T10:19:51Z
dc.date.available2010-04-07T10:19:51Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3873
dc.language.isoenen
dc.subjectNon-local equationen
dc.subjectHigher order equationen
dc.subjectHydraulic fracturesen
dc.subjectperiodic Hilbert transformen
dc.subjectNon-negative solutionsen
dc.subjectThin film equationen
dc.subject.ddc515en
dc.titleExistence of solutions for a higher order non-local equation appearing in crack dynamicsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we prove the existence of non-negative solutions for a non-local third order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann type operator (which can be defined using the periodic Hilbert transform). The main difficulties are due to the fact that this equation is non-local, and that the natural energy estimates are not as good as in the case of the thin film equation.en
dc.relation.isversionofjnlnameNonlinearity
dc.relation.isversionofjnlvol24
dc.relation.isversionofjnlissue12
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpagesPaper 3487
dc.relation.isversionofdoihttp://dx.doi.org/10.1088/0951-7715/24/12/008
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00451017/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherIOP Science
dc.subject.ddclabelAnalyseen


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