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Phasefield theory for fractional diffusion-reaction equations and applications

dc.contributor.authorImbert, Cyril
HAL ID: 9368
ORCID: 0000-0002-1290-8257
dc.contributor.authorSouganidis, Panagiotis E.
dc.date.accessioned2011-10-14T08:45:31Z
dc.date.available2011-10-14T08:45:31Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7218
dc.language.isoenen
dc.subjectfractional diffusion-reaction equationsen
dc.subjecttraveling waveen
dc.subjectphasefield theoryen
dc.subjectanisotropic mean curvature motionen
dc.subjectfractional Laplacianen
dc.subjectGreen-Kubo type formulaeen
dc.subject.ddc515en
dc.titlePhasefield theory for fractional diffusion-reaction equations and applicationsen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper is concerned with diffusion-reaction equations where the classical diffusion term, such as the Laplacian operator, is replaced with a singular integral term, such as the fractional Laplacian operator. As far as the reaction term is concerned, we consider bistable non-linearities. After properly rescaling (in time and space) these integro-differential evolution equations, we show that the limits of their solutions as the scaling parameter goes to zero exhibit interfaces moving by anisotropic mean curvature. The singularity and the unbounded support of the potential at stake are both the novelty and the challenging difficulty of this work.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages41en
dc.identifier.urlsitehttp://arxiv.org/abs/0907.5524v1en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen


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