Show simple item record

Fast Diffusion leads to partial mass concentration in Keller-Segel type stationary solutions

hal.structure.identifierMathematical Institute [Oxford] [MI]
dc.contributor.authorCarrillo, José A.
hal.structure.identifierCalifornian Institute of Technology [Caltech]
hal.structure.identifierPontifícia Universidade Católica do Rio de Janeiro [PUC-Rio]
dc.contributor.authorDelgadino, Matias G.
hal.structure.identifierMathematisches Institut [München] [LMU]
dc.contributor.authorFrank, Rupert L.
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLewin, Mathieu
dc.date.accessioned2021-12-07T13:07:34Z
dc.date.available2021-12-07T13:07:34Z
dc.date.issued2022
dc.identifier.issn0218-2025
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22332
dc.language.isoenen
dc.subjectKeller–Segel
dc.subjectaggregation–diffusion
dc.subjectmass concentration
dc.subject.ddc520en
dc.titleFast Diffusion leads to partial mass concentration in Keller-Segel type stationary solutions
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe show that partial mass concentration can happen for stationary solutions of aggregation–diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction potential, we find the exact range of the diffusion exponent where concentration occurs in space dimensions N≥6. We then provide numerical computations which suggest the occurrence of mass concentration in all dimensions N≥3, for homogeneous interaction potentials with higher power.
dc.relation.isversionofjnlnameMathematical Models and Methods in Applied Sciences (M3AS)
dc.relation.isversionofjnlvol32
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2022
dc.relation.isversionofjnlpages831-850
dc.relation.isversionofdoi10.1142/S021820252250018X
dc.relation.isversionofjnlpublisherWorld Scientific
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-04T10:04:04Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail
Name:
2012.08586.pdf
Size:
290.7Kb
Format:
PDF
View/Open

This item appears in the following Collection(s)

Show simple item record