# On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics

Hdl Handle:
http://hdl.handle.net/10034/620247
Title:
On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics
Authors:
Kavallaris, Nikos I.; Lankeit, Johannes; Winkler, Michael
Abstract:
We 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.
Affiliation:
Citation:
Kavallaris, 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: 10.1137/15M1053840
Publisher:
SIAM
Journal:
SIAM Journal on Mathematical Analysis
Publication Date:
Nov-2016
URI:
http://hdl.handle.net/10034/620247
DOI:
10.1137/15M1053840
http://epubs.siam.org/doi/abs/10.1137/15M1053840
Type:
Article
Language:
en
ISSN:
0036-1410
Appears in Collections:
Mathematics

DC FieldValue Language
dc.contributor.authorKavallaris, Nikos I.en
dc.contributor.authorLankeit, Johannesen
dc.contributor.authorWinkler, Michaelen
dc.date.accessioned2016-11-08T17:11:58Z-
dc.date.available2016-11-08T17:11:58Z-
dc.date.issued2016-11-
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.en
dc.language.isoenen
dc.publisherSIAMen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/15M1053840en
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.identifier.journalSIAM Journal on Mathematical Analysisen
dc.date.accepted2016-11-01-
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen