On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics
dc.contributor.author | Kavallaris, Nikos I. | * |
dc.contributor.author | Lankeit, Johannes | * |
dc.contributor.author | Winkler, Michael | * |
dc.date.accessioned | 2016-11-08T17:11:58Z | |
dc.date.available | 2016-11-08T17:11:58Z | |
dc.date.issued | 2017-03-28 | |
dc.identifier.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 | en |
dc.identifier.issn | 0036-1410 | |
dc.identifier.doi | 10.1137/15M1053840 | |
dc.identifier.uri | http://hdl.handle.net/10034/620247 | |
dc.description.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. | |
dc.language.iso | en | en |
dc.publisher | SIAM | en |
dc.relation.url | http://epubs.siam.org/doi/abs/10.1137/15M1053840 | en |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | en |
dc.subject | Degenerate diffusion | en |
dc.subject | Non-local nonlinearity | en |
dc.subject | Blow-up | en |
dc.subject | Evolutionary games | en |
dc.subject | Infinite dimensional replicator dynamics | en |
dc.title | On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics | en |
dc.type | Article | en |
dc.contributor.department | University of Chester; Paderborn University | en |
dc.identifier.journal | SIAM Journal on Mathematical Analysis | |
dc.date.accepted | 2016-10-31 | |
or.grant.openaccess | Yes | en |
rioxxterms.funder | Unfunded | en |
rioxxterms.identifier.project | Unfunded | en |
rioxxterms.version | AM | en |
rioxxterms.versionofrecord | https://doi.org/10.1137/15M1053840 | |
rioxxterms.licenseref.startdate | 2017-03-28 | |
html.description.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. | |
rioxxterms.publicationdate | 2017-03-28 |