Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, f...
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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10780947_v31_n2_p581_Terra http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_10780947_v31_n2_p581_Terra_oai |
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I28-R145-paper_10780947_v31_n2_p581_Terra_oai2020-10-19 Terra, J. Wolanski, N. 2011 We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, for which we prove that tff=2ju(x; t) , U(x; t)j → 0 where U is the solution of the heat equation with absorption with initial datum U(x; 0) = CA;N |x|,α. Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u0 in the supercritical case and also in the critical case (p = 1 + 2=N) for bounded and integrable u0. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_10780947_v31_n2_p581_Terra info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Discrete Contin. Dyn. Syst. 2011;31(2):581-605 Large time behavior Nonlocal diffusion Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_10780947_v31_n2_p581_Terra_oai |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-145 |
collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
topic |
Large time behavior Nonlocal diffusion |
spellingShingle |
Large time behavior Nonlocal diffusion Terra, J. Wolanski, N. Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
topic_facet |
Large time behavior Nonlocal diffusion |
description |
We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, for which we prove that tff=2ju(x; t) , U(x; t)j → 0 where U is the solution of the heat equation with absorption with initial datum U(x; 0) = CA;N |x|,α. Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u0 in the supercritical case and also in the critical case (p = 1 + 2=N) for bounded and integrable u0. |
format |
Artículo Artículo publishedVersion |
author |
Terra, J. Wolanski, N. |
author_facet |
Terra, J. Wolanski, N. |
author_sort |
Terra, J. |
title |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
title_short |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
title_full |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
title_fullStr |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
title_full_unstemmed |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
title_sort |
large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
publishDate |
2011 |
url |
http://hdl.handle.net/20.500.12110/paper_10780947_v31_n2_p581_Terra http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_10780947_v31_n2_p581_Terra_oai |
work_keys_str_mv |
AT terraj largetimebehaviorforanonlocaldiffusionequationwithabsorptionandboundedinitialdata AT wolanskin largetimebehaviorforanonlocaldiffusionequationwithabsorptionandboundedinitialdata |
_version_ |
1766026751181324288 |