Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case

In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity...

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Autores principales: Terra, J., Wolanski, N.
Formato: JOUR
Materias:
Boundary value problems
Nonlocal diffusion
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v139_n4_p1421_Terra
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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_00029939_v139_n4_p1421_Terra2023-10-03T13:55:12Z Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case Terra, J. Wolanski, N. Boundary value problems Nonlocal diffusion In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum. © 2010 American Mathematical Society. Fil:Wolanski, N. 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_00029939_v139_n4_p1421_Terra
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Boundary value problems
Nonlocal diffusion
spellingShingle Boundary value problems
Nonlocal diffusion
Terra, J.
Wolanski, N.
Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
topic_facet Boundary value problems
Nonlocal diffusion
description In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum. © 2010 American Mathematical Society.
format JOUR
author Terra, J.
Wolanski, N.
author_facet Terra, J.
Wolanski, N.
author_sort Terra, J.
title Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
title_short Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
title_full Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
title_fullStr Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
title_full_unstemmed Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
title_sort asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. the supercritical case
url http://hdl.handle.net/20.500.12110/paper_00029939_v139_n4_p1421_Terra
work_keys_str_mv AT terraj asymptoticbehaviorforanonlocaldiffusionequationwithabsorptionandnonintegrableinitialdatathesupercriticalcase
AT wolanskin asymptoticbehaviorforanonlocaldiffusionequationwithabsorptionandnonintegrableinitialdatathesupercriticalcase
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