Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation

We consider a two dimensional parabolic–elliptic Keller–Segel equation with a fractional diffusion of order and a logistic term. In the case of an analogous problem with standard diffusion, introduction of the logistic term, well motivated by biological applications, results in global smoothness of...

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Authors: Burczak, Jan, Granero Belinchón, Rafael|||0000-0003-2752-8086
Format: article
Publication Date:2017
Country:España
Institution:Universidad de Cantabria (UC)
Repository:UCrea Repositorio Abierto de la Universidad de Cantabria
Language:English
OAI Identifier:oai:repositorio.unican.es:10902/29582
Online Access:https://hdl.handle.net/10902/29582
Access Level:Open access
Keyword:Keller–Segel System
Fractional Dissipation
Global-In-Time Smoothness
Logistic Source
Nonlocal Maximum Principle
Active Scalar Equations
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spelling Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipationBurczak, JanGranero Belinchón, Rafael|||0000-0003-2752-8086Keller–Segel SystemFractional DissipationGlobal-In-Time SmoothnessLogistic SourceNonlocal Maximum PrincipleActive Scalar EquationsWe consider a two dimensional parabolic–elliptic Keller–Segel equation with a fractional diffusion of order and a logistic term. In the case of an analogous problem with standard diffusion, introduction of the logistic term, well motivated by biological applications, results in global smoothness of solutions (i.e. suppression of blowup), compare Tello & Winkler [48]. We show that this phenomenon extends into potentially less regular case of fractional diffusions. Namely, we obtain existence of global in time regular solutions emanating from initial data with no size restrictions for , where depends on the equation's parameters. For an even wider range of , we prove existence of global in time weak solution for general initial data.JB is partially supported by the internal IMPAN grant for young researchers. RGB is supported by the Labex MILYON and the Grant MTM2014-59488-P from the Ministerio de Economía y Competitividad (MINECO, Spain). Part of the research leading to results presented here was conducted during a short stay of RGB at IMPAN within WCMCS KNOW framework.ElsevierUniversidad de Cantabria20172017-11-05journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/29582Journal of Differential Equations, 2017, 263(9), 6115-6142reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/295822026-06-02T12:39:31Z
dc.title.none.fl_str_mv Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
title Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
spellingShingle Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
Burczak, Jan
Keller–Segel System
Fractional Dissipation
Global-In-Time Smoothness
Logistic Source
Nonlocal Maximum Principle
Active Scalar Equations
title_short Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
title_full Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
title_fullStr Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
title_full_unstemmed Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
title_sort Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation
dc.creator.none.fl_str_mv Burczak, Jan
Granero Belinchón, Rafael|||0000-0003-2752-8086
author Burczak, Jan
author_facet Burczak, Jan
Granero Belinchón, Rafael|||0000-0003-2752-8086
author_role author
author2 Granero Belinchón, Rafael|||0000-0003-2752-8086
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Keller–Segel System
Fractional Dissipation
Global-In-Time Smoothness
Logistic Source
Nonlocal Maximum Principle
Active Scalar Equations
topic Keller–Segel System
Fractional Dissipation
Global-In-Time Smoothness
Logistic Source
Nonlocal Maximum Principle
Active Scalar Equations
description We consider a two dimensional parabolic–elliptic Keller–Segel equation with a fractional diffusion of order and a logistic term. In the case of an analogous problem with standard diffusion, introduction of the logistic term, well motivated by biological applications, results in global smoothness of solutions (i.e. suppression of blowup), compare Tello & Winkler [48]. We show that this phenomenon extends into potentially less regular case of fractional diffusions. Namely, we obtain existence of global in time regular solutions emanating from initial data with no size restrictions for , where depends on the equation's parameters. For an even wider range of , we prove existence of global in time weak solution for general initial data.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-11-05
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/29582
url https://hdl.handle.net/10902/29582
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Journal of Differential Equations, 2017, 263(9), 6115-6142
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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