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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Autor principal: Wolanski, Noemi Irene
Publicado: 2011
Materias:
Boundary value problems
Nonlocal diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v139_n4_p1421_Terra
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 paper:paper_00029939_v139_n4_p1421_Terra2023-06-08T14:23:31Z Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case Wolanski, Noemi Irene 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v139_n4_p1421_Terra 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
Wolanski, Noemi Irene
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.
author Wolanski, Noemi Irene
author_facet Wolanski, Noemi Irene
author_sort Wolanski, Noemi Irene
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
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v139_n4_p1421_Terra
http://hdl.handle.net/20.500.12110/paper_00029939_v139_n4_p1421_Terra
work_keys_str_mv AT wolanskinoemiirene asymptoticbehaviorforanonlocaldiffusionequationwithabsorptionandnonintegrableinitialdatathesupercriticalcase
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