A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass

Kavallaris, Nikos I.; Ricciardi, Tonia; Zecca, Gabriela

dc.contributor.author	Kavallaris, Nikos I.	*
dc.contributor.author	Ricciardi, Tonia	*
dc.contributor.author	Zecca, Gabriela	*
dc.date.accessioned	2017-11-03T14:40:26Z
dc.date.available	2017-11-03T14:40:26Z
dc.date.issued	2017-10-09
dc.identifier.citation	Kavallaris, N. I., Ricciardi, T., & Zecca, G. (2018). A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass. European Journal of Applied Mathematics, 29(3), 515-542. http://doi.org/10.1017/S0956792517000286	en
dc.identifier.doi	10.1017/S0956792517000286
dc.identifier.uri	http://hdl.handle.net/10034/620705
dc.description	This article has been accepted for publication and will appear in a revised form, subsequent to peer review and/or editorial input by Cambridge University Press, in European Journal of Applied Mathematics published by Cambridge University Press. Copyright Cambridge University Press 2017.	en
dc.description.abstract	We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted vs.\ repelled by a single chemical substance. The production vs.\ destruction rates of the chemotactic substance by the species is described by a probability measure. For such a model we investigate the variational structures, in particular we prove the existence of Lyapunov functionals, we establish duality properties as well as a logarithmic Hardy-Littlewood-Sobolev type inequality for the associated free energy. The latter inequality provides the optimal critical value for the conserved total population mass.
dc.language.iso	en	en
dc.publisher	Cambridge University Press	en
dc.relation.url	https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	en
dc.subject	Multi-species chemotaxis models	en
dc.subject	Lyapunov functionals	en
dc.subject	Duality	en
dc.subject	Logarithmic 20 Hardy–Littlewood–Sobolev inequality	en
dc.subject	Moser–Trudinger inequality	en
dc.title	A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass	en
dc.type	Article	en
dc.identifier.eissn	1469-4425
dc.contributor.department	University of Chester; Universita` di Napoli Federico II	en
dc.identifier.journal	European Journal of Applied Mathematics
dc.date.accepted	2017-09-20
or.grant.openaccess	Yes	en
rioxxterms.funder	PRIN 2012 74FYK7 005 and GNAMPA-INDAM 2015 “Alcuni aspetti di equazioni ellittiche non-lineari”	en
rioxxterms.identifier.project	PRIN 2012 74FYK7 005	en
rioxxterms.identifier.project	GNAMPA-INDAM 2015 “Alcuni aspetti di equazioni ellittiche non-lineari”	en
rioxxterms.version	AM	en
rioxxterms.licenseref.startdate	2018-04-09
html.description.abstract	We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted vs.\ repelled by a single chemical substance. The production vs.\ destruction rates of the chemotactic substance by the species is described by a probability measure. For such a model we investigate the variational structures, in particular we prove the existence of Lyapunov functionals, we establish duality properties as well as a logarithmic Hardy-Littlewood-Sobolev type inequality for the associated free energy. The latter inequality provides the optimal critical value for the conserved total population mass.
rioxxterms.publicationdate	2017-10-09