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Abstract:

In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation (Formula presented.), with v(x, t) = g(x, t), (Formula presented.) can be approximated uniformly by solutions of nonlocal problems of the form (Formula presented.), with (Formula presented.) , (Formula presented.) , as (Formula presented.) , for an appropriate rescaled kernel (Formula presented.). In this way, we show that the usual local evolution problems with spatial dependence can be approximated by nonlocal ones. In the case of an equation in divergence form, we can obtain an approximation with symmetric kernels, that is, (Formula presented.). © 2016, Springer International Publishing.

Registro:

Documento: Artículo
Título:Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
Autor:Molino, A.; Rossi, J.D.
Filiación:Departamento de Análisis Matemático, Campus Fuentenueva S/N, Universidad de Granada, Granada, 18071, Spain
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina
Palabras clave:Evolution problems; Nonlocal diffusion; Spacial dependence; Mathematical techniques; Dirichlet problem; Evolution problem; Nonlocal diffusion; Nonlocal problems; Parabolic Equations; Spacial dependence; Spatial dependence; Symmetric kernel; Partial differential equations
Año:2016
Volumen:67
Número:3
DOI: http://dx.doi.org/10.1007/s00033-016-0649-8
Título revista:Zeitschrift fur Angewandte Mathematik und Physik
Título revista abreviado:Z. Angew. Math. Phys.
ISSN:00442275
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00442275_v67_n3_p_Molino

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Citas:

---------- APA ----------
Molino, A. & Rossi, J.D. (2016) . Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence. Zeitschrift fur Angewandte Mathematik und Physik, 67(3).
http://dx.doi.org/10.1007/s00033-016-0649-8
---------- CHICAGO ----------
Molino, A., Rossi, J.D. "Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence" . Zeitschrift fur Angewandte Mathematik und Physik 67, no. 3 (2016).
http://dx.doi.org/10.1007/s00033-016-0649-8
---------- MLA ----------
Molino, A., Rossi, J.D. "Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence" . Zeitschrift fur Angewandte Mathematik und Physik, vol. 67, no. 3, 2016.
http://dx.doi.org/10.1007/s00033-016-0649-8
---------- VANCOUVER ----------
Molino, A., Rossi, J.D. Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence. Z. Angew. Math. Phys. 2016;67(3).
http://dx.doi.org/10.1007/s00033-016-0649-8