Continuous time random walks and the Cauchy problem for the heat equation
- Autores
- Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela
- Año de publicación
- 2018
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We deal with anomalous diffusions induced by continuous time random walks - CTRW in ℝn. A particle moves in ℝn in such a way that the probability density function u(·, t) of finding it in region Ω of ℝn is given by ∫Ωu(x, t)dx. The dynamics of the diffusion is provided by a space time probability density J(x, t) compactly supported in {t ≥ 0}. For t large enough, u satisfies the equation u(x, t) = [ (J− δ) * u] (x, t) , where δ is the Dirac delta in space-time. We give a sense to a Cauchy type problem for a given initial density distribution f. We use Banach fixed point method to solve it and prove that under parabolic rescaling of J, the equation tends weakly to the heat equation and that for particular kernels J, the solutions tend to the corresponding temperatures when the scaling parameter approaches 0.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Beltritti, Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina - Materia
-
Heat equation
Continuous time random walks - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/88694
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Continuous time random walks and the Cauchy problem for the heat equationAimar, Hugo AlejandroBeltritti, GastónGomez, Ivana DanielaHeat equationContinuous time random walkshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We deal with anomalous diffusions induced by continuous time random walks - CTRW in ℝn. A particle moves in ℝn in such a way that the probability density function u(·, t) of finding it in region Ω of ℝn is given by ∫Ωu(x, t)dx. The dynamics of the diffusion is provided by a space time probability density J(x, t) compactly supported in {t ≥ 0}. For t large enough, u satisfies the equation u(x, t) = [ (J− δ) * u] (x, t) , where δ is the Dirac delta in space-time. We give a sense to a Cauchy type problem for a given initial density distribution f. We use Banach fixed point method to solve it and prove that under parabolic rescaling of J, the equation tends weakly to the heat equation and that for particular kernels J, the solutions tend to the corresponding temperatures when the scaling parameter approaches 0.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Beltritti, Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaSpringer2018-10info: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/11336/88694Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela; Continuous time random walks and the Cauchy problem for the heat equation; Springer; Journal d'Analyse Mathématique; 136; 1; 10-2018; 83-1010021-7670CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11854-018-0056-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:48:53Zoai:ri.conicet.gov.ar:11336/88694instacron: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 09:48:53.667CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Continuous time random walks and the Cauchy problem for the heat equation |
title |
Continuous time random walks and the Cauchy problem for the heat equation |
spellingShingle |
Continuous time random walks and the Cauchy problem for the heat equation Aimar, Hugo Alejandro Heat equation Continuous time random walks |
title_short |
Continuous time random walks and the Cauchy problem for the heat equation |
title_full |
Continuous time random walks and the Cauchy problem for the heat equation |
title_fullStr |
Continuous time random walks and the Cauchy problem for the heat equation |
title_full_unstemmed |
Continuous time random walks and the Cauchy problem for the heat equation |
title_sort |
Continuous time random walks and the Cauchy problem for the heat equation |
dc.creator.none.fl_str_mv |
Aimar, Hugo Alejandro Beltritti, Gastón Gomez, Ivana Daniela |
author |
Aimar, Hugo Alejandro |
author_facet |
Aimar, Hugo Alejandro Beltritti, Gastón Gomez, Ivana Daniela |
author_role |
author |
author2 |
Beltritti, Gastón Gomez, Ivana Daniela |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Heat equation Continuous time random walks |
topic |
Heat equation Continuous time random walks |
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 deal with anomalous diffusions induced by continuous time random walks - CTRW in ℝn. A particle moves in ℝn in such a way that the probability density function u(·, t) of finding it in region Ω of ℝn is given by ∫Ωu(x, t)dx. The dynamics of the diffusion is provided by a space time probability density J(x, t) compactly supported in {t ≥ 0}. For t large enough, u satisfies the equation u(x, t) = [ (J− δ) * u] (x, t) , where δ is the Dirac delta in space-time. We give a sense to a Cauchy type problem for a given initial density distribution f. We use Banach fixed point method to solve it and prove that under parabolic rescaling of J, the equation tends weakly to the heat equation and that for particular kernels J, the solutions tend to the corresponding temperatures when the scaling parameter approaches 0. Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Beltritti, Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina |
description |
We deal with anomalous diffusions induced by continuous time random walks - CTRW in ℝn. A particle moves in ℝn in such a way that the probability density function u(·, t) of finding it in region Ω of ℝn is given by ∫Ωu(x, t)dx. The dynamics of the diffusion is provided by a space time probability density J(x, t) compactly supported in {t ≥ 0}. For t large enough, u satisfies the equation u(x, t) = [ (J− δ) * u] (x, t) , where δ is the Dirac delta in space-time. We give a sense to a Cauchy type problem for a given initial density distribution f. We use Banach fixed point method to solve it and prove that under parabolic rescaling of J, the equation tends weakly to the heat equation and that for particular kernels J, the solutions tend to the corresponding temperatures when the scaling parameter approaches 0. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-10 |
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/11336/88694 Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela; Continuous time random walks and the Cauchy problem for the heat equation; Springer; Journal d'Analyse Mathématique; 136; 1; 10-2018; 83-101 0021-7670 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/88694 |
identifier_str_mv |
Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela; Continuous time random walks and the Cauchy problem for the heat equation; Springer; Journal d'Analyse Mathématique; 136; 1; 10-2018; 83-101 0021-7670 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11854-018-0056-5 |
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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13.069144 |