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Abstract:

In this paper we study the applicability of energy methods to obtain bounds for the asymptotic decay of solutions to nonlocal diffusion problems. With these energy methods we can deal with nonlocal problems that not necessarily involve a convolution, that is, of the form ut (x, t) = ∫Rd G (x - y) (u (y, t) - u (x, t)) d y. For example, we will consider equations like,ut (x, t) = under(∫, Rd) J (x, y) (u (y, t) - u (x, t)) d y + f (u) (x, t), and a nonlocal analogous to the p-Laplacian,ut (x, t) = under(∫, Rd) J (x, y) | u (y, t) - u (x, t) |p - 2 (u (y, t) - u (x, t)) d y . The energy method developed here allows us to obtain decay rates of the form,{norm of matrix} u (ṡ, t) {norm of matrix}Lq (Rd) ≤ C t- α, for some explicit exponent α that depends on the parameters, d, q and p, according to the problem under consideration. © 2009 Elsevier Masson SAS. All rights reserved.

Registro:

Documento: Artículo
Título:Decay estimates for nonlocal problems via energy methods
Autor:Ignat, L.I.; Rossi, J.D.
Filiación:Institute of Mathematics Simion Stoilow, the Romanian Academy, PO Box 1-764, RO-014700 Bucharest, Romania
Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Energy methods; Nonlocal diffusion; p-Laplacian
Año:2009
Volumen:92
Número:2
Página de inicio:163
Página de fin:187
DOI: http://dx.doi.org/10.1016/j.matpur.2009.04.009
Título revista:Journal des Mathematiques Pures et Appliquees
Título revista abreviado:J. Math. Pures Appl.
ISSN:00217824
CODEN:JMPAA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00217824_v92_n2_p163_Ignat.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v92_n2_p163_Ignat

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Citas:

---------- APA ----------
Ignat, L.I. & Rossi, J.D. (2009) . Decay estimates for nonlocal problems via energy methods. Journal des Mathematiques Pures et Appliquees, 92(2), 163-187.
http://dx.doi.org/10.1016/j.matpur.2009.04.009
---------- CHICAGO ----------
Ignat, L.I., Rossi, J.D. "Decay estimates for nonlocal problems via energy methods" . Journal des Mathematiques Pures et Appliquees 92, no. 2 (2009) : 163-187.
http://dx.doi.org/10.1016/j.matpur.2009.04.009
---------- MLA ----------
Ignat, L.I., Rossi, J.D. "Decay estimates for nonlocal problems via energy methods" . Journal des Mathematiques Pures et Appliquees, vol. 92, no. 2, 2009, pp. 163-187.
http://dx.doi.org/10.1016/j.matpur.2009.04.009
---------- VANCOUVER ----------
Ignat, L.I., Rossi, J.D. Decay estimates for nonlocal problems via energy methods. J. Math. Pures Appl. 2009;92(2):163-187.
http://dx.doi.org/10.1016/j.matpur.2009.04.009