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Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorBrandle Cerqueira, Cristina
dc.contributor.authorPablo Martínez, Arturo de
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.date.accessioned2021-12-14T09:36:33Z
dc.date.available2021-12-14T09:36:33Z
dc.date.issued2018-05
dc.description.abstractWe study the short and large time behaviour of solutions of nonlocal heat equations of the form ∂tu+Lu=0. Here L is an integral operator given by a symmetric nonnegative kernel of Lévy type, that includes bounded and unbounded transition probability densities. We characterize when a regularizing effect occurs for small times and obtain Lq-Lp decay estimates, 1≤q<p<∞ when the time is large. These properties turn out to depend only on the behaviour of the kernel at the origin or at infinity, respectively, without need of any information at the other end. An equivalence between the decay and a restricted Nash inequality is shown. Finally we deal with the decay of nonlinear nonlocal equations of porous medium type ∂tu+LΦ(u)=0.en
dc.description.sponsorshipWork partially supported by Spanish project MTM2011-25287.en
dc.format.extent18
dc.identifier.bibliographicCitationBrändle, C. & Pablo, A. de (2018). Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities. Communications on Pure & Applied Analysis, 17(3), 1161–1178.en
dc.identifier.doihttps://doi.org/10.3934/cpaa.2018056
dc.identifier.issn1534-0392
dc.identifier.publicationfirstpage1161
dc.identifier.publicationissue3
dc.identifier.publicationlastpage1178
dc.identifier.publicationtitleCommunications on Pure & Applied Analysisen
dc.identifier.publicationvolume17
dc.identifier.urihttps://hdl.handle.net/10016/33755
dc.identifier.uxxiAR/0000021700
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.relation.projectIDGobierno de España. MTM2011-25287es
dc.rights© 2018 American Institute of Mathematical Sciencesen
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherNonlocal diffusion equationsen
dc.subject.otherIntegral operatorsen
dc.subject.otherAsymptotic behaviouren
dc.subject.otherNash inequalitiesen
dc.titleNonlocal heat equations: Regularizing effect, decay estimates and Nash inequalitiesen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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