Asymptotic behaviour for a semilinear nonlocal equation

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 e...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Rossi, Julio Daniel
Publicado:	2007
Materias:	Asymptotic behaviour Nonlocal diffusion Semilinear problems Approximation theory Finite element method Linear equations Asymptotic behavior Asymptotic analysis
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto http://hdl.handle.net/20.500.12110/paper_09217134_v52_n1-2_p143_Pazoto
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_09217134_v52_n1-2_p143_Pazoto
record_format	dspace
spelling	paper:paper_09217134_v52_n1-2_p143_Pazoto2023-06-08T15:50:48Z Asymptotic behaviour for a semilinear nonlocal equation Rossi, Julio Daniel Asymptotic behaviour Nonlocal diffusion Semilinear problems Approximation theory Finite element method Linear equations Asymptotic behavior Nonlocal diffusion Semilinear problems Asymptotic analysis 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto http://hdl.handle.net/20.500.12110/paper_09217134_v52_n1-2_p143_Pazoto
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Asymptotic behaviour Nonlocal diffusion Semilinear problems Approximation theory Finite element method Linear equations Asymptotic behavior Nonlocal diffusion Semilinear problems Asymptotic analysis
spellingShingle	Asymptotic behaviour Nonlocal diffusion Semilinear problems Approximation theory Finite element method Linear equations Asymptotic behavior Nonlocal diffusion Semilinear problems Asymptotic analysis Rossi, Julio Daniel Asymptotic behaviour for a semilinear nonlocal equation
topic_facet	Asymptotic behaviour Nonlocal diffusion Semilinear problems Approximation theory Finite element method Linear equations Asymptotic behavior Nonlocal diffusion Semilinear problems Asymptotic analysis
description	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.
author	Rossi, Julio Daniel
author_facet	Rossi, Julio Daniel
author_sort	Rossi, Julio Daniel
title	Asymptotic behaviour for a semilinear nonlocal equation
title_short	Asymptotic behaviour for a semilinear nonlocal equation
title_full	Asymptotic behaviour for a semilinear nonlocal equation
title_fullStr	Asymptotic behaviour for a semilinear nonlocal equation
title_full_unstemmed	Asymptotic behaviour for a semilinear nonlocal equation
title_sort	asymptotic behaviour for a semilinear nonlocal equation
publishDate	2007
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto http://hdl.handle.net/20.500.12110/paper_09217134_v52_n1-2_p143_Pazoto
work_keys_str_mv	AT rossijuliodaniel asymptoticbehaviourforasemilinearnonlocalequation
_version_	1768541618272468992

Asymptotic behaviour for a semilinear nonlocal equation

Ejemplares similares