A nonlocal diffusion problem on manifolds

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...

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Detalles Bibliográficos
Publicado: 2018
Materias:
Diffusion on manifolds
hyperbolic space
localization
longtime behavior
nonlocal diffusion
spectral properties
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v43_n4_p652_Bandle
http://hdl.handle.net/20.500.12110/paper_03605302_v43_n4_p652_Bandle
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03605302_v43_n4_p652_Bandle
record_format dspace
spelling paper:paper_03605302_v43_n4_p652_Bandle2023-06-08T15:34:48Z A nonlocal diffusion problem on manifolds Diffusion on manifolds hyperbolic space localization longtime behavior nonlocal diffusion spectral properties 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. © 2018, © 2018 Taylor & Francis. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v43_n4_p652_Bandle http://hdl.handle.net/20.500.12110/paper_03605302_v43_n4_p652_Bandle
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Diffusion on manifolds
hyperbolic space
localization
longtime behavior
nonlocal diffusion
spectral properties
spellingShingle Diffusion on manifolds
hyperbolic space
localization
longtime behavior
nonlocal diffusion
spectral properties
A nonlocal diffusion problem on manifolds
topic_facet Diffusion on manifolds
hyperbolic space
localization
longtime behavior
nonlocal diffusion
spectral properties
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. © 2018, © 2018 Taylor & Francis.
title A nonlocal diffusion problem on manifolds
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 nonlocal diffusion problem on manifolds
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v43_n4_p652_Bandle
http://hdl.handle.net/20.500.12110/paper_03605302_v43_n4_p652_Bandle
_version_ 1768544041686794240

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