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dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.contributor.authorJankowiak, Gaspard
HAL ID: 2027
ORCID: 0000-0002-9025-1465
dc.contributor.authorMarkowich, Peter
dc.date.accessioned2013-05-23T06:58:52Z
dc.date.available2013-05-23T06:58:52Z
dc.date.issued2015
dc.identifier.issn2326-7186
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11287
dc.language.isoenen
dc.subjectherding
dc.subjectdynamical stability
dc.subjectcrowd motion
dc.subjectcontinuum model
dc.subjectvariational methods
dc.subjectnon self-adjoint evolution operators
dc.subjectLyapunov functional
dc.subject.ddc515en
dc.titleStationary solutions of Keller-Segel type crowd motion and herding models: multiplicity and dynamical stability
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Applied Mathematics and Theoretical Physics (DAMTP) University of Cambridge;Royaume-Uni
dc.description.abstractenIn this paper we study two models for crowd motion and herding. Each of the models is of Keller-Segel type and involves two parabolic equations, one for the evolution of the density and one for the evolution of a mean field potential. We classify all radial stationary solutions, prove multiplicity results and establish some qualitative properties of these solutions, which are characterized as critical points of an energy functional. A notion of variational stability is associated to such solutions. The dynamical stability in a neighborhood of a stationary solution is also studied in terms of the spectral properties of the linearized evolution operator. For one of the two models, we exhibit a Lyapunov functional which allows to make the link between the two notions of stability. Even in that case, for certain values of the mass parameter and all other parameters taken in an appropriate range, we find that two dynamically stable stationary solutions exist. We further discuss qualitative properties of the solutions using theoretical methods and numerical computations.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameMathematics and mechanics of complex systems
dc.relation.isversionofjnlvol3
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages211-242
dc.relation.isversionofdoi10.2140/memocs.2015.3.211
dc.identifier.urlsitehttps://arxiv.org/abs/1305.1715v2
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-10-06T15:26:48Z


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