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Fast diffusion flow on manifolds of nonpositive curvature

hal.structure.identifier
dc.contributor.authorBonforte, Matteo*
hal.structure.identifier
dc.contributor.authorGrillo, Gabriele*
hal.structure.identifier
dc.contributor.authorVazquez, Juan-Luis*
dc.date.accessioned2014-03-27T12:44:50Z
dc.date.available2014-03-27T12:44:50Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12966
dc.language.isoenen
dc.subjectNonlinear evolutionsen
dc.subjectsingular parabolic equationsen
dc.subjectfast diffusionen
dc.subjectRiemannian manifoldsen
dc.subjectasymptoticsen
dc.subject.ddc515en
dc.titleFast diffusion flow on manifolds of nonpositive curvatureen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the fast diffusion equation (FDE) u t = Δu m (0 < m < 1) on a nonparabolic Riemannian manifold M. Existence of weak solutions holds. Then we show that the validity of Euclidean–type Sobolev inequalities implies that certain L p −L q smoothing effects of the type ∥u(t)∥ q ≤ Ct −α ∥u 0∥γ p , the case q = ∞ being included. The converse holds if m is sufficiently close to one. We then consider the case in which the manifold has the addition gap property min σ(−Δ) > 0. In that case solutions vanish in finite time, and we estimate from below and from above the extinction time.en
dc.relation.isversionofjnlnameJournal of Evolution Equations
dc.relation.isversionofjnlvol8en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages99-128en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00028-007-0345-4en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
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