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Fractional semi-linear parabolic equations with unbounded data

dc.contributor.authorAlibaud, Nathaël
HAL ID: 5327
dc.contributor.authorImbert, Cyril
HAL ID: 9368
ORCID: 0000-0002-1290-8257
dc.date.accessioned2009-07-06T14:52:56Z
dc.date.available2009-07-06T14:52:56Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/838
dc.language.isoenen
dc.subjectintegro-differential Hamilton-Jacobi equationen
dc.subjectunbounded dataen
dc.subjectunbounded solutionsen
dc.subjectfinite-infinite propagation speeden
dc.subjectnon-local regularizationen
dc.subjectLévy operatoren
dc.subjectviscosity solutionen
dc.subjectconvergence of the gradientsen
dc.subject.ddc519en
dc.titleFractional semi-linear parabolic equations with unbounded dataen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherCNRS - Université de Montpellier II - Sciences et Techniques du Languedoc;France
dc.description.abstractenThis paper is devoted to the study of semi-linear parabolic equations whose principal term is fractional, i.e. is integral and eventually singular. A typical example is the fractional Laplace operator. This work sheds light on the fact that, if the initial datum is not bounded, assumptions on the non-linearity are closely related to its behavior at infinity. The sub-linear and super-linear cases are first treated by classical techniques. We next present a third original case: if the associated first order Hamilton-Jacobi equation is such that perturbations propagate at finite speed, then the semi-linear parabolic equation somehow keeps memory of this property. By using such a result, locally bounded initial data that are merely integrable at infinity can be handled. Next, regularity of the solution is proved. Eventually, strong convergence of gradients as the fractional term disappears is proved for strictly convex non-linearity.en
dc.relation.isversionofjnlnameTransactions of the American Mathematical Society
dc.relation.isversionofjnlvol361en
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages2527-2566en
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0002-9947-08-04758-2
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00144548/en/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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