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

Hdl Handle:
http://hdl.handle.net/10034/620705
Title:
A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass
Authors:
Kavallaris, Nikos I.; Ricciardi, Tonia; Zecca, Gabriela
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.
Affiliation:
University of Chester; Universita` di Napoli Federico II
Citation:
Kavallaris, N. I., Ricciardi, T., & Zecca, G. (2017 - in press). A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass. European Journal of Applied Mathematics.
Publisher:
Cambridge University Press
Journal:
European Journal of Applied Mathematics
Publication Date:
9-Oct-2017
URI:
http://hdl.handle.net/10034/620705
DOI:
10.1017/S0956792517000286
Additional Links:
https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/
Type:
Article
Language:
en
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.
EISSN:
1469-4425
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorKavallaris, Nikos I.en
dc.contributor.authorRicciardi, Toniaen
dc.contributor.authorZecca, Gabrielaen
dc.date.accessioned2017-11-03T14:40:26Z-
dc.date.available2017-11-03T14:40:26Z-
dc.date.issued2017-10-09-
dc.identifier.citationKavallaris, N. I., Ricciardi, T., & Zecca, G. (2017 - in press). A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass. European Journal of Applied Mathematics.en
dc.identifier.doi10.1017/S0956792517000286-
dc.identifier.urihttp://hdl.handle.net/10034/620705-
dc.descriptionThis 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.abstractWe 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.en
dc.language.isoenen
dc.publisherCambridge University Pressen
dc.relation.urlhttps://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectMulti-species chemotaxis modelsen
dc.subjectLyapunov functionalsen
dc.subjectDualityen
dc.subjectLogarithmic 20 Hardy–Littlewood–Sobolev inequalityen
dc.subjectMoser–Trudinger inequalityen
dc.titleA multi-species chemotaxis system: Lyapunov functionals, duality, critical massen
dc.typeArticleen
dc.identifier.eissn1469-4425-
dc.contributor.departmentUniversity of Chester; Universita` di Napoli Federico IIen
dc.identifier.journalEuropean Journal of Applied Mathematicsen
dc.date.accepted2017-09-20-
or.grant.openaccessYesen
rioxxterms.funderPRIN 2012 74FYK7 005 and GNAMPA-INDAM 2015 “Alcuni aspetti di equazioni ellittiche non-lineari”en
rioxxterms.identifier.projectPRIN 2012 74FYK7 005en
rioxxterms.identifier.projectGNAMPA-INDAM 2015 “Alcuni aspetti di equazioni ellittiche non-lineari”en
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2018-04-09-
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