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Abstract:

We study the semilinear nonlocal equation u t =Ju-u-u p in the whole. First, we prove the global well-posedness for initial conditions. Next, we obtain the long time behaviour of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J: finite time extinction for p<1, faster than exponential decay for the linear case p=1, a weakly nonlinear behaviour for p large enough and a decay governed by the nonlinear term when p is greater than one but not so large. © 2007 - IOS Press and the authors. All rights reserved.

Registro:

Documento: Artículo
Título:Asymptotic behaviour for a semilinear nonlocal equation
Autor:Pazoto, A.F.; Rossi, J.D.
Filiación:Instituto de Matemática, Universidade Federal do Rio de Janeiro (UFRJ), Cidade Universitária, P.O. Box 68530, CEP 21945-970, Rio de Janeiro, Brazil
Depto. Matemática, FCEyN UBA, Pab I, 1428 Buenos Aires, Argentina
Palabras clave:Asymptotic behaviour; Nonlocal diffusion; Semilinear problems; Approximation theory; Finite element method; Linear equations; Asymptotic behavior; Nonlocal diffusion; Semilinear problems; Asymptotic analysis
Año:2007
Volumen:52
Número:1-2
Página de inicio:143
Página de fin:155
Título revista:Asymptotic Analysis
Título revista abreviado:Asymptotic Anal
ISSN:09217134
CODEN:ASANE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto

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Citas:

---------- APA ----------
Pazoto, A.F. & Rossi, J.D. (2007) . Asymptotic behaviour for a semilinear nonlocal equation. Asymptotic Analysis, 52(1-2), 143-155.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto [ ]
---------- CHICAGO ----------
Pazoto, A.F., Rossi, J.D. "Asymptotic behaviour for a semilinear nonlocal equation" . Asymptotic Analysis 52, no. 1-2 (2007) : 143-155.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto [ ]
---------- MLA ----------
Pazoto, A.F., Rossi, J.D. "Asymptotic behaviour for a semilinear nonlocal equation" . Asymptotic Analysis, vol. 52, no. 1-2, 2007, pp. 143-155.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto [ ]
---------- VANCOUVER ----------
Pazoto, A.F., Rossi, J.D. Asymptotic behaviour for a semilinear nonlocal equation. Asymptotic Anal. 2007;52(1-2):143-155.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto [ ]