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...

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Autores principales: Pazoto, A.F., Rossi, J.D.
Formato: JOUR
Materias:
Asymptotic behaviour
Nonlocal diffusion
Semilinear problems
Approximation theory
Finite element method
Linear equations
Asymptotic behavior
Asymptotic analysis
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09217134_v52_n1-2_p143_Pazoto
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_09217134_v52_n1-2_p143_Pazoto2023-10-03T15:45:39Z Asymptotic behaviour for a semilinear nonlocal equation Pazoto, A.F. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Pazoto, A.F.
Rossi, J.D.
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.
format JOUR
author Pazoto, A.F.
Rossi, J.D.
author_facet Pazoto, A.F.
Rossi, J.D.
author_sort Pazoto, A.F.
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
url http://hdl.handle.net/20.500.12110/paper_09217134_v52_n1-2_p143_Pazoto
work_keys_str_mv AT pazotoaf asymptoticbehaviourforasemilinearnonlocalequation
AT rossijd asymptoticbehaviourforasemilinearnonlocalequation
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