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Abstract:

study the large time behavior of solutions to the nonlocal diffusion equation ℓtu = J-u-u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ζ1 ≤ |x|t.1/2 ≤ ζ2, ζ1, ζ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R.: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t1/2h(t), limt→h(t) = 0, the solution scaled by a factor t3/2/(|x| + 1) converges to a stationary solution of the problem that behaves as b±x as x ±. The constants b± are obtained through a matching procedure with the far field limit. In the very far field, |x|≤t1/2g(t), g(t)→, the solution decays as o(t-1). © by SIAM.

Registro:

Documento: Artículo
Título:Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
Autor:Cortazar, C.; Elgueta, M.; Quiros, F.; Wolanski, N.
Filiación:Departamento de Matematica, Pontificia Universidad Catolica de Chile, Santiago, 7820436, Chile
Departamento de Matematicas, Universidad Autonoma de Madrid, Madrid, 28049, Spain
Departamento de Matematica, FCEyN, UBA, IMAS, CONICET, Ciudad Universitaria, Pab. I, Buenos Aires, 1428, Argentina
Palabras clave:Asymptotic behavior; Exterior domain; Matched asymptotics; Nonlocal diffusion; Asymptotic analysis; Diffusion; Asymptotic behaviors; Dirichlet data; Exterior domain; First moments; Large time behavior; Matched asymptotics; Nonlocal diffusion; Stationary solutions; Partial differential equations
Año:2016
Volumen:48
Número:3
Página de inicio:1549
Página de fin:1574
DOI: http://dx.doi.org/10.1137/151006287
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.
ISSN:00361410
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v48_n3_p1549_Cortazar

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Citas:

---------- APA ----------
Cortazar, C., Elgueta, M., Quiros, F. & Wolanski, N. (2016) . Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains. SIAM Journal on Mathematical Analysis, 48(3), 1549-1574.
http://dx.doi.org/10.1137/151006287
---------- CHICAGO ----------
Cortazar, C., Elgueta, M., Quiros, F., Wolanski, N. "Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains" . SIAM Journal on Mathematical Analysis 48, no. 3 (2016) : 1549-1574.
http://dx.doi.org/10.1137/151006287
---------- MLA ----------
Cortazar, C., Elgueta, M., Quiros, F., Wolanski, N. "Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains" . SIAM Journal on Mathematical Analysis, vol. 48, no. 3, 2016, pp. 1549-1574.
http://dx.doi.org/10.1137/151006287
---------- VANCOUVER ----------
Cortazar, C., Elgueta, M., Quiros, F., Wolanski, N. Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains. SIAM J. Math. Anal. 2016;48(3):1549-1574.
http://dx.doi.org/10.1137/151006287