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dc.contributor.authorLafleche, Laurent*
dc.contributor.authorSalem, Samir*
dc.date.accessioned2019-02-21T10:21:53Z
dc.date.available2019-02-21T10:21:53Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18472
dc.language.isoenen
dc.subjectKeller-Segel Equation
dc.subjectAnalysis of PDEs
dc.subject.ddc519en
dc.titleFractional Keller-Segel Equation: Global Well-posedness and Finite Time Blow-up
dc.title.alternativeÉquation de Keller-Segel fractionnaire : Existence et unicité globales et explosion en temps fini
dc.typeDocument de travail / Working paper
dc.description.abstractenThis article studies the aggregation diffusion equation ∂ρ/∂t = ∆^(α/2) ρ + λ div((K * ρ)ρ), where ∆^(α/2) denotes the fractional Laplacian and K = x/|x|^a is an attractive kernel. This equation is a generalization of the classical Keller-Segel equation, which arises in the modeling of the motion of cells. In the diffusion dominated case a < α we prove global well-posedness for an L^1_k initial condition, and in the fair competition case a = α for an L^1_k ∩ L ln L initial condition. In the aggregation dominated case a > α, we prove global or local well posedness for an L^p initial condition, depending on some smallness condition on the L^p norm of the initial condition. We also prove that finite time blow-up of even solutions occurs, under some initial mass concentration criteria.
dc.identifier.citationpages30
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01875506
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2019-02-21T10:31:48Z
hal.person.labIds60*
hal.person.labIds60*


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