Artículo
Gómez, C.A.; Rossi, J.D. "A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions" (2017) Journal of King Saud University - Science
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Abstract:
In this paper we discuss a nonlocal approximation to the classical heat equation with Neumann boundary conditions. We consider. wt(small element of)(x,t)=1(small element of)N+2∫ΩJx-y(small element of)(w(small element of)(y,t)-w(small element of)(x,t))dy+C1(small element of)N∫∂ΩJx-y(small element of)g(y,t)dSy,(x,t)∈Ω[U+203E]×(0,T),w(x,0)=u0(x),x∈Ω[U+203E],and we show that the corresponding solutions, w(small element of), converge to the classical solution of the local heat equation vt=δv with Neumann boundary conditions, ∂v∂n(x,t)=g(x,t), and initial condition v(0)=u0, as the parameter (small element of) goes to zero. The obtained convergence is in the weak star on L∞ topology. © 2017 The Authors.
Registro:
| Documento: | Artículo |
| Título: | A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| Autor: | Gómez, C.A.; Rossi, J.D. |
| Filiación: | Department of Mathematics, National University of Colombia, Bogotá, Colombia Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria. Pab 1, 1428 Buenos Aires, Argentina |
| Palabras clave: | 35K05; 45A05; 45J05; Heat equation; Neumann boundary conditions; Nonlocal diffusion |
| Año: | 2017 |
| DOI: | http://dx.doi.org/10.1016/j.jksus.2017.08.008 |
| Título revista: | Journal of King Saud University - Science |
| Título revista abreviado: | J. King Saud Univ. Sci. |
| ISSN: | 10183647 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10183647_v_n_p_Gomez |
Citas:
---------- APA ----------
Gómez, C.A. & Rossi, J.D. (2017) . A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions. Journal of King Saud University - Science.http://dx.doi.org/10.1016/j.jksus.2017.08.008
---------- CHICAGO ----------
Gómez, C.A., Rossi, J.D. "A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions" . Journal of King Saud University - Science (2017).http://dx.doi.org/10.1016/j.jksus.2017.08.008
---------- MLA ----------
Gómez, C.A., Rossi, J.D. "A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions" . Journal of King Saud University - Science, 2017.http://dx.doi.org/10.1016/j.jksus.2017.08.008
---------- VANCOUVER ----------
Gómez, C.A., Rossi, J.D. A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions. J. King Saud Univ. Sci. 2017.http://dx.doi.org/10.1016/j.jksus.2017.08.008
