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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03605302_v43_n4_p652_Bandle |
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todo:paper_03605302_v43_n4_p652_Bandle2023-10-03T15:26:37Z A nonlocal diffusion problem on manifolds Bandle, C. González, M.D.M. Fontelos, M.A. Wolanski, N. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Bandle, C. González, M.D.M. Fontelos, M.A. Wolanski, N. 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. |
| format |
JOUR |
| author |
Bandle, C. González, M.D.M. Fontelos, M.A. Wolanski, N. |
| author_facet |
Bandle, C. González, M.D.M. Fontelos, M.A. Wolanski, N. |
| author_sort |
Bandle, C. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_03605302_v43_n4_p652_Bandle |
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1807316774141558784 |