A nonlocal diffusion problem on manifolds

Autores
Bandle, Catherine; González, María del Mar; Fontelos, Marco A.; Wolanski, Noemi Irene
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior.
Fil: Bandle, Catherine. University Of Basel; Suiza
Fil: González, María del Mar. Universidad Autonoma de Madrid; España
Fil: Fontelos, Marco A.. Instituto de Ciencias Matemáticas; España
Fil: Wolanski, Noemi Irene. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
DIFFUSION ON MANIFOLDS
HYPERBOLIC SPACE
LOCALIZATION
LONGTIME BEHAVIOR
NONLOCAL DIFFUSION
SPECTRAL PROPERTIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/89053
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A nonlocal diffusion problem on manifoldsBandle, CatherineGonzález, María del MarFontelos, Marco A.Wolanski, Noemi IreneDIFFUSION ON MANIFOLDSHYPERBOLIC SPACELOCALIZATIONLONGTIME BEHAVIORNONLOCAL DIFFUSIONSPECTRAL PROPERTIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior.Fil: Bandle, Catherine. University Of Basel; SuizaFil: González, María del Mar. Universidad Autonoma de Madrid; EspañaFil: Fontelos, Marco A.. Instituto de Ciencias Matemáticas; EspañaFil: Wolanski, Noemi Irene. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaTaylor & Francis2018-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/89053Bandle, Catherine; González, María del Mar; Fontelos, Marco A.; Wolanski, Noemi Irene; A nonlocal diffusion problem on manifolds; Taylor & Francis; Communications In Partial Differential Equations; 43; 4; 4-2018; 652-6760360-5302CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1510.09190info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/03605302.2018.1459685?journalCode=lpde20info:eu-repo/semantics/altIdentifier/doi/10.1080/03605302.2018.1459685info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:46:02Zoai:ri.conicet.gov.ar:11336/89053instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:46:02.864CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A nonlocal diffusion problem on manifolds
title A nonlocal diffusion problem on manifolds
spellingShingle A nonlocal diffusion problem on manifolds
Bandle, Catherine
DIFFUSION ON MANIFOLDS
HYPERBOLIC SPACE
LOCALIZATION
LONGTIME BEHAVIOR
NONLOCAL DIFFUSION
SPECTRAL PROPERTIES
title_short A nonlocal diffusion problem on manifolds
title_full A nonlocal diffusion problem on manifolds
title_fullStr A nonlocal diffusion problem on manifolds
title_full_unstemmed A nonlocal diffusion problem on manifolds
title_sort A nonlocal diffusion problem on manifolds
dc.creator.none.fl_str_mv Bandle, Catherine
González, María del Mar
Fontelos, Marco A.
Wolanski, Noemi Irene
author Bandle, Catherine
author_facet Bandle, Catherine
González, María del Mar
Fontelos, Marco A.
Wolanski, Noemi Irene
author_role author
author2 González, María del Mar
Fontelos, Marco A.
Wolanski, Noemi Irene
author2_role author
author
author
dc.subject.none.fl_str_mv DIFFUSION ON MANIFOLDS
HYPERBOLIC SPACE
LOCALIZATION
LONGTIME BEHAVIOR
NONLOCAL DIFFUSION
SPECTRAL PROPERTIES
topic DIFFUSION ON MANIFOLDS
HYPERBOLIC SPACE
LOCALIZATION
LONGTIME BEHAVIOR
NONLOCAL DIFFUSION
SPECTRAL PROPERTIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior.
Fil: Bandle, Catherine. University Of Basel; Suiza
Fil: González, María del Mar. Universidad Autonoma de Madrid; España
Fil: Fontelos, Marco A.. Instituto de Ciencias Matemáticas; España
Fil: Wolanski, Noemi Irene. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior.
publishDate 2018
dc.date.none.fl_str_mv 2018-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/89053
Bandle, Catherine; González, María del Mar; Fontelos, Marco A.; Wolanski, Noemi Irene; A nonlocal diffusion problem on manifolds; Taylor & Francis; Communications In Partial Differential Equations; 43; 4; 4-2018; 652-676
0360-5302
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89053
identifier_str_mv Bandle, Catherine; González, María del Mar; Fontelos, Marco A.; Wolanski, Noemi Irene; A nonlocal diffusion problem on manifolds; Taylor & Francis; Communications In Partial Differential Equations; 43; 4; 4-2018; 652-676
0360-5302
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1510.09190
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/03605302.2018.1459685?journalCode=lpde20
info:eu-repo/semantics/altIdentifier/doi/10.1080/03605302.2018.1459685
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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