Artículo

Bandle, C.; González, M.D.M.; Fontelos, M.A.; Wolanski, N. "A nonlocal diffusion problem on manifolds" (2018) Communications in Partial Differential Equations. 43(4):652-676
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Abstract:

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.

Registro:

Documento: Artículo
Título:A nonlocal diffusion problem on manifolds
Autor:Bandle, C.; González, M.D.M.; Fontelos, M.A.; Wolanski, N.
Filiación:Department of Mathematics, University of Basel, Basel, Switzerland
Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
Instituto de Ciencias Matemáticas, Madrid, Spain
Departamento de Matemática, FCEyN-UBA and IMAS, CONICET Ciudad Universitaria, Buenos Aires, Argentina
Palabras clave:Diffusion on manifolds; hyperbolic space; localization; longtime behavior; nonlocal diffusion; spectral properties
Año:2018
Volumen:43
Número:4
Página de inicio:652
Página de fin:676
DOI: http://dx.doi.org/10.1080/03605302.2018.1459685
Título revista:Communications in Partial Differential Equations
Título revista abreviado:Commun. Partial Differ. Equ.
ISSN:03605302
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v43_n4_p652_Bandle

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Citas:

---------- APA ----------
Bandle, C., González, M.D.M., Fontelos, M.A. & Wolanski, N. (2018) . A nonlocal diffusion problem on manifolds. Communications in Partial Differential Equations, 43(4), 652-676.
http://dx.doi.org/10.1080/03605302.2018.1459685
---------- CHICAGO ----------
Bandle, C., González, M.D.M., Fontelos, M.A., Wolanski, N. "A nonlocal diffusion problem on manifolds" . Communications in Partial Differential Equations 43, no. 4 (2018) : 652-676.
http://dx.doi.org/10.1080/03605302.2018.1459685
---------- MLA ----------
Bandle, C., González, M.D.M., Fontelos, M.A., Wolanski, N. "A nonlocal diffusion problem on manifolds" . Communications in Partial Differential Equations, vol. 43, no. 4, 2018, pp. 652-676.
http://dx.doi.org/10.1080/03605302.2018.1459685
---------- VANCOUVER ----------
Bandle, C., González, M.D.M., Fontelos, M.A., Wolanski, N. A nonlocal diffusion problem on manifolds. Commun. Partial Differ. Equ. 2018;43(4):652-676.
http://dx.doi.org/10.1080/03605302.2018.1459685