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Abstract:

We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u t = J*u - u in the whole ℝ with an initial condition u(x, 0) = u 0(x). Under suitable hypotheses on J (involving its Fourier transform) and u 0, it is proved an expansion of the form equation is presented where K t is the regular part of the fundamental solution and the exponent A depends on J, q, k and the dimension d. Moreover, we can obtain bounds for the difference between the terms in this expansion and the corresponding ones for the expansion of the evolution given by fractional powers of the Laplacian, ν-t (x, t) = -(-Δ) 2ν (x, t). © 2008 Birkhaueser.

Registro:

Documento: Artículo
Título:Refined asymptotic expansions for nonlocal diffusion equations
Autor:Ignat, L.I.; Rossi, J.D.
Filiación:Institute of Mathematics, Romanian Academy, P.O. Box 1-764, Bucharest RO-014700, Romania
IMDEA Matematicas, C-IX, Campus UAM, Madrid, Spain
Departamento de Matemática, FCEyN UBA, Buenos Aires 1428, Argentina
Palabras clave:Asymptotic behavior; Fractional Laplacian; Nonlocal diffusion
Año:2008
Volumen:8
Número:4
Página de inicio:617
Página de fin:629
DOI: http://dx.doi.org/10.1007/s00028-008-0372-9
Título revista:Journal of Evolution Equations
Título revista abreviado:J. Evol. Equ.
ISSN:14243199
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n4_p617_Ignat

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Citas:

---------- APA ----------
Ignat, L.I. & Rossi, J.D. (2008) . Refined asymptotic expansions for nonlocal diffusion equations. Journal of Evolution Equations, 8(4), 617-629.
http://dx.doi.org/10.1007/s00028-008-0372-9
---------- CHICAGO ----------
Ignat, L.I., Rossi, J.D. "Refined asymptotic expansions for nonlocal diffusion equations" . Journal of Evolution Equations 8, no. 4 (2008) : 617-629.
http://dx.doi.org/10.1007/s00028-008-0372-9
---------- MLA ----------
Ignat, L.I., Rossi, J.D. "Refined asymptotic expansions for nonlocal diffusion equations" . Journal of Evolution Equations, vol. 8, no. 4, 2008, pp. 617-629.
http://dx.doi.org/10.1007/s00028-008-0372-9
---------- VANCOUVER ----------
Ignat, L.I., Rossi, J.D. Refined asymptotic expansions for nonlocal diffusion equations. J. Evol. Equ. 2008;8(4):617-629.
http://dx.doi.org/10.1007/s00028-008-0372-9