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dc.contributor.authorKavallaris, Nikos I.*
dc.contributor.authorLankeit, Johannes*
dc.contributor.authorWinkler, Michael*
dc.date.accessioned2016-11-08T17:11:58Z
dc.date.available2016-11-08T17:11:58Z
dc.date.issued2017-03-28
dc.identifier.citationKavallaris, N. I., Lankeit, J., & Winkler, M. (2017). On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics. SIAM Journal on Mathematical Analysis, 49(2), 954-983. DOI: 10.1137/15M1053840en
dc.identifier.issn0036-1410
dc.identifier.doi10.1137/15M1053840
dc.identifier.urihttp://hdl.handle.net/10034/620247
dc.description.abstractWe establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u \Delta u + u \int_\Omega |\nabla u|^2 \] in bounded domains $\Om\sub\R^n$ which arises in game theory. We prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global.
dc.language.isoenen
dc.publisherSIAMen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/15M1053840en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectDegenerate diffusionen
dc.subjectNon-local nonlinearityen
dc.subjectBlow-upen
dc.subjectEvolutionary gamesen
dc.subjectInfinite dimensional replicator dynamicsen
dc.titleOn a degenerate non-local parabolic problem describing infinite dimensional replicator dynamicsen
dc.typeArticleen
dc.contributor.departmentUniversity of Chester; Paderborn Universityen
dc.identifier.journalSIAM Journal on Mathematical Analysis
dc.date.accepted2016-10-31
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.versionofrecordhttps://doi.org/10.1137/15M1053840
rioxxterms.licenseref.startdate2017-03-28
html.description.abstractWe establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u \Delta u + u \int_\Omega |\nabla u|^2 \] in bounded domains $\Om\sub\R^n$ which arises in game theory. We prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global.
rioxxterms.publicationdate2017-03-28


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