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dc.contributor.authorLafleche, Laurent
dc.date.accessioned2018-09-03T08:58:19Z
dc.date.available2018-09-03T08:58:19Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17920
dc.language.isoenen
dc.subjectfractional Laplacian
dc.subjectFokker-Planck
dc.subjectfractional diffusion with drift
dc.subjectconfinement force
dc.subjectasymptotic behavior
dc.subject.ddc515en
dc.titleFractional Fokker-Planck Equation with General Confinement Force
dc.typeDocument de travail / Working paper
dc.description.abstractenThis article studies a Fokker-Planck type equation of fractional diffusion with conservative drift ∂f/∂t = ∆^(α/2) f + div(Ef), where ∆^(α/2) denotes the fractional Laplacian and E is a confining force field. The main interest of the present paper is that it applies to a wide variety of force fields, with a few local regularity and a polynomial growth at infinity. We first prove the existence and uniqueness of a solution in weighted Lebesgue spaces depending on E under the form of a strongly continuous semigroup. We also prove the existence and uniqueness of a stationary state, by using an appropriate splitting of the fractional Laplacian and by proving a weak and strong maximum principle. We then study the rate of convergence to equilibrium of the solution. The semigroup has a property of regularization in fractional Sobolev spaces, as well as a gain of integrability and positivity which we use to obtain polynomial or exponential convergence to equilibrium in weighted Lebesgue spaces.
dc.identifier.citationpages31
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2018-09-03T09:02:19Z
hal.person.labIds60


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