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dc.contributor.authorSchmeiser, Christian
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2009-07-13T08:24:06Z
dc.date.available2009-07-13T08:24:06Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/1099
dc.language.isoenen
dc.subjectKeller-Segelen
dc.subjectchemotaxis
dc.subjectblow-up
dc.subjectaggregation
dc.subjectmeasure valued solutions
dc.subjectdefect measure
dc.subject.ddc519en
dc.titleThe two-dimensional Keller-Segel model after blow-upen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversität Wien;Autriche
dc.description.abstractenIn the two-dimensional Keller-Segel model for chemotaxis of biological cells, blow-up of solutions in finite time occurs if the total mass is above a critical value. Blow-up is a concentration event, where point aggregates are created. In this work global existence of generalized solutions is proven, allowing for measure valued densities. This extends the solution concept after blow-up. The existence result is an application of a theory developed by Poupaud, where the cell distribution is characterized by an additional defect measure, which vanishes for smooth cell densities. The global solutions are constructed as limits of solutions of a regularized problem. A strong formulation is derived under the assumption that the generalized solution consists of a smooth part and a number of smoothly varying point aggregates. Comparison with earlier formal asymptotic results shows that the choice of a solution concept after blow-up is not unique and depends on the type of regularization. This work is also concerned with local density profiles close to point aggregates. An equation for these profiles is derived by passing to the limit in a rescaled version of the regularized model. Solvability of the profile equation can also be obtained by minimizing a free energy functional.en
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnlvol25en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages109-121
dc.relation.isversionofdoihttp://dx.doi.org/10.3934/dcds.2009.25.109
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00158767/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Institute of Mathematical Sciencesen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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