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Blow-up and global existence for a kinetic equation of swarm formation

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cris.lastimport.scopus2024-02-12T20:04:01Z
dc.abstract.enIn this paper we study a kinetic equation that describes swarm formations. The right hand side of this equation contains nonlinear integro-differential terms responsible for two opposite tendencies: dissipation and swarming. The nonlinear integral operator describes the changes of velocities (orientations) of interacting individuals. The interaction rate is assumed to be dependent of velocities of interacting individuals. Although the equation seems to be rather simple it leads to very complicated dynamics. In this paper, we study possible blow-ups versus global existence of solutions and provide results on the asymptotic behavior. The complicated dynamics and possibility of blow-ups can be directly related to creation of swarms.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorParisot, Martin
dc.contributor.authorLachowicz, Mirosław
dc.contributor.authorLeszczyński, Henryk
dc.date.accessioned2024-01-24T18:40:10Z
dc.date.available2024-01-24T18:40:10Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.number6
dc.description.volume27
dc.identifier.doi10.1142/S0218202517400115
dc.identifier.issn0218-2025
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/102389
dc.identifier.weblinkhttps://www.worldscientific.com/doi/abs/10.1142/S0218202517400115
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofMathematical Models and Methods in Applied Sciences
dc.relation.pages1153-1175
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enBlow-upglobal
dc.subject.enexistencekinetic
dc.subject.enequationsswarms
dc.titleBlow-up and global existence for a kinetic equation of swarm formation
dc.typeJournalArticle
dspace.entity.typePublication