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Cortázar, C.; Elgueta, M.; Quirós, F.; Wolanski, N. "Asymptotic behavior for a nonlocal diffusion equation on the half line" (2015) Discrete and Continuous Dynamical Systems- Series A. 35(4):1391-1407
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Abstract:

We study the large time behavior of solutions to a nonlocal diffusion equation, ut = J ∗ u-u with J smooth, radially symmetric and compactly supported, posed in ℝ+ with zero Dirichlet boundary conditions. In the far-field scale, ξ1 ≤ xt-1/2 ≤ ξ2 with ξ1, ξ2 > 0, the asymptotic behavior is given by a multiple of the dipole solution for the local heat equation, hence tu(x, t) is bounded above and below by positive constants in this region for large times. The proportionality constant is determined from a conservation law, related to the asymptotic first momentum. In compact sets, after scaling the solution by a factor t3/2, it converges to a multiple of the unique stationary solution of the problem that behaves as x at infinity. The precise proportionality factor is obtained through a matching procedure with the far-field limit. Finally, in the very far-field, x ≥ t1/2g(t) with g(t) → ∞, the solution is proved to be of order o(t-1).

Registro:

Documento: Artículo
Título:Asymptotic behavior for a nonlocal diffusion equation on the half line
Autor:Cortázar, C.; Elgueta, M.; Quirós, F.; Wolanski, N.
Filiación:Departamento de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile
Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, 28049, Spain
Departamento de Matemática, UBA, CONICET Ciudad Universitaria, Pab. I, Buenos Aires, 1428, Argentina
Palabras clave:Asymptotic behavior; Matched asymptotics; Nonlocal diffusion
Año:2015
Volumen:35
Número:4
Página de inicio:1391
Página de fin:1407
DOI: http://dx.doi.org/10.3934/dcds.2015.35.1391
Título revista:Discrete and Continuous Dynamical Systems- Series A
Título revista abreviado:Discrete Contin. Dyn. Syst. Ser A
ISSN:10780947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v35_n4_p1391_Cortazar

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Citas:

---------- APA ----------
Cortázar, C., Elgueta, M., Quirós, F. & Wolanski, N. (2015) . Asymptotic behavior for a nonlocal diffusion equation on the half line. Discrete and Continuous Dynamical Systems- Series A, 35(4), 1391-1407.
http://dx.doi.org/10.3934/dcds.2015.35.1391
---------- CHICAGO ----------
Cortázar, C., Elgueta, M., Quirós, F., Wolanski, N. "Asymptotic behavior for a nonlocal diffusion equation on the half line" . Discrete and Continuous Dynamical Systems- Series A 35, no. 4 (2015) : 1391-1407.
http://dx.doi.org/10.3934/dcds.2015.35.1391
---------- MLA ----------
Cortázar, C., Elgueta, M., Quirós, F., Wolanski, N. "Asymptotic behavior for a nonlocal diffusion equation on the half line" . Discrete and Continuous Dynamical Systems- Series A, vol. 35, no. 4, 2015, pp. 1391-1407.
http://dx.doi.org/10.3934/dcds.2015.35.1391
---------- VANCOUVER ----------
Cortázar, C., Elgueta, M., Quirós, F., Wolanski, N. Asymptotic behavior for a nonlocal diffusion equation on the half line. Discrete Contin. Dyn. Syst. Ser A. 2015;35(4):1391-1407.
http://dx.doi.org/10.3934/dcds.2015.35.1391