Nonlocal heat equations in the Heisenberg group

Autores
Vidal, Raúl Emilio
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the parabolic equation for the fractional laplace operator. To obtain this result we use the spherical transform related to the pair (U(n) , Hn). Finally we prove that solutions of properly rescaled nonlocal Dirichlet problem converge uniformly to the solution of the corresponding Dirichlet problem for the classical heat equation in the Heisenberg group.
Fil: Vidal, Raúl Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
HEISENBERG GROUP
NONLOCAL DIFFUSION
SPHERICAL TRANSFORM
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:11336/59992
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59992
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nonlocal heat equations in the Heisenberg groupVidal, Raúl EmilioHEISENBERG GROUPNONLOCAL DIFFUSIONSPHERICAL TRANSFORMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the parabolic equation for the fractional laplace operator. To obtain this result we use the spherical transform related to the pair (U(n) , Hn). Finally we prove that solutions of properly rescaled nonlocal Dirichlet problem converge uniformly to the solution of the corresponding Dirichlet problem for the classical heat equation in the Heisenberg group.Fil: Vidal, Raúl Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaSpringer2017-10info: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/11336/59992Vidal, Raúl Emilio; Nonlocal heat equations in the Heisenberg group; Springer; Nonlinear Differential Equations And Applications; 24; 5; 10-2017; 1-211021-9722CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00030-017-0479-1info:eu-repo/semantics/altIdentifier/doi/10.1007/s00030-017-0479-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:55:04Zoai:ri.conicet.gov.ar:11336/59992instacron: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:34982025-09-17 11:55:05.045CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonlocal heat equations in the Heisenberg group
title Nonlocal heat equations in the Heisenberg group
spellingShingle Nonlocal heat equations in the Heisenberg group
Vidal, Raúl Emilio
HEISENBERG GROUP
NONLOCAL DIFFUSION
SPHERICAL TRANSFORM
title_short Nonlocal heat equations in the Heisenberg group
title_full Nonlocal heat equations in the Heisenberg group
title_fullStr Nonlocal heat equations in the Heisenberg group
title_full_unstemmed Nonlocal heat equations in the Heisenberg group
title_sort Nonlocal heat equations in the Heisenberg group
dc.creator.none.fl_str_mv Vidal, Raúl Emilio
author Vidal, Raúl Emilio
author_facet Vidal, Raúl Emilio
author_role author
dc.subject.none.fl_str_mv HEISENBERG GROUP
NONLOCAL DIFFUSION
SPHERICAL TRANSFORM
topic HEISENBERG GROUP
NONLOCAL DIFFUSION
SPHERICAL TRANSFORM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the parabolic equation for the fractional laplace operator. To obtain this result we use the spherical transform related to the pair (U(n) , Hn). Finally we prove that solutions of properly rescaled nonlocal Dirichlet problem converge uniformly to the solution of the corresponding Dirichlet problem for the classical heat equation in the Heisenberg group.
Fil: Vidal, Raúl Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the parabolic equation for the fractional laplace operator. To obtain this result we use the spherical transform related to the pair (U(n) , Hn). Finally we prove that solutions of properly rescaled nonlocal Dirichlet problem converge uniformly to the solution of the corresponding Dirichlet problem for the classical heat equation in the Heisenberg group.
publishDate 2017
dc.date.none.fl_str_mv 2017-10
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/11336/59992
Vidal, Raúl Emilio; Nonlocal heat equations in the Heisenberg group; Springer; Nonlinear Differential Equations And Applications; 24; 5; 10-2017; 1-21
1021-9722
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59992
identifier_str_mv Vidal, Raúl Emilio; Nonlocal heat equations in the Heisenberg group; Springer; Nonlinear Differential Equations And Applications; 24; 5; 10-2017; 1-21
1021-9722
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://link.springer.com/article/10.1007%2Fs00030-017-0479-1
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00030-017-0479-1
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 Springer
publisher.none.fl_str_mv Springer
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 13.001348

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