Global solutions for a supercritical drift-diffusion equation

We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order...

Descripción completa

Detalles Bibliográficos
Autores: Burczak, Jan, Granero Belinchón, Rafael|||0000-0003-2752-8086
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/30386
Acceso en línea:https://hdl.handle.net/10902/30386
Access Level:acceso abierto
Palabra clave:Drift–diffusion equation
Nonlocal diffusion
Global existence
id ES_fbe0ce330c43cc37d97823f22e7dcf9f
oai_identifier_str oai:repositorio.unican.es:10902/30386
network_acronym_str ES
network_name_str España
repository_id_str
spelling Global solutions for a supercritical drift-diffusion equationBurczak, JanGranero Belinchón, Rafael|||0000-0003-2752-8086Drift–diffusion equationNonlocal diffusionGlobal existenceWe study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order of the fractional diffusion α∈(1-c1, 2], where c1>0 is an explicit constant depending on the physical parameters present in the problem (chemosensitivity and strength of logistic damping). Furthermore, in the range 1-c2<α≤2 with 0<c2<c1, the solution is globally smooth. Let us emphasize that when α<1, the diffusion is in the supercritical regime.RGB is partially supported by the Department of Mathematics at University of California, Davis.ElsevierUniversidad de Cantabria20162016-06-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/30386Advances in Mathematics, 2016, 295, 334-367reponame: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:10902/303862026-06-02T12:39:31Z
dc.title.none.fl_str_mv Global solutions for a supercritical drift-diffusion equation
title Global solutions for a supercritical drift-diffusion equation
spellingShingle Global solutions for a supercritical drift-diffusion equation
Burczak, Jan
Drift–diffusion equation
Nonlocal diffusion
Global existence
title_short Global solutions for a supercritical drift-diffusion equation
title_full Global solutions for a supercritical drift-diffusion equation
title_fullStr Global solutions for a supercritical drift-diffusion equation
title_full_unstemmed Global solutions for a supercritical drift-diffusion equation
title_sort Global solutions for a supercritical drift-diffusion equation
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 Drift–diffusion equation
Nonlocal diffusion
Global existence
topic Drift–diffusion equation
Nonlocal diffusion
Global existence
description We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order of the fractional diffusion α∈(1-c1, 2], where c1>0 is an explicit constant depending on the physical parameters present in the problem (chemosensitivity and strength of logistic damping). Furthermore, in the range 1-c2<α≤2 with 0<c2<c1, the solution is globally smooth. Let us emphasize that when α<1, the diffusion is in the supercritical regime.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-06-01
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/10902/30386
url https://hdl.handle.net/10902/30386
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 Advances in Mathematics, 2016, 295, 334-367
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
_version_ 1869425370362544128
score 15,301603

Similares en LA Referencia