Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem

We obtain upper bounds for the decay rate for solutions to the nonlocal problem λtu(x, t) = ∫ℝn J(x, y)|u(y, t) - u(x, t)|p-2(u(y, t) - u(x, t)) dy with an initial condition u0 ε L1(ℝn) ∩ L(Rn) and a fixed p > 2. We assume that the kernel J is symmetric, bounded (and therefore there is no reg...

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Autor principal: Rossi, Julio Daniel
Publicado: 2014
Materias:
Decay rates
Nonlocal diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16872762_v2014_n_p_Esteve
http://hdl.handle.net/20.500.12110/paper_16872762_v2014_n_p_Esteve
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_16872762_v2014_n_p_Esteve
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spelling paper:paper_16872762_v2014_n_p_Esteve2023-06-08T16:26:40Z Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem Rossi, Julio Daniel Decay rates Nonlocal diffusion We obtain upper bounds for the decay rate for solutions to the nonlocal problem λtu(x, t) = ∫ℝn J(x, y)|u(y, t) - u(x, t)|p-2(u(y, t) - u(x, t)) dy with an initial condition u0 ε L1(ℝn) ∩ L(Rn) and a fixed p > 2. We assume that the kernel J is symmetric, bounded (and therefore there is no regularizing effect) but with polynomial tails, that is, we assume a lower bounds of the form J(x, y) ≥ c1|x - y|-(n+2λ), for |x - y| c2 and J(x, y) . c1, for |x - y| ≤ c2. We prove that (eqution presented) for q ≥ 1 and t large. © 2014 Esteve et al. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16872762_v2014_n_p_Esteve http://hdl.handle.net/20.500.12110/paper_16872762_v2014_n_p_Esteve
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Decay rates
Nonlocal diffusion
spellingShingle Decay rates
Nonlocal diffusion
Rossi, Julio Daniel
Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
topic_facet Decay rates
Nonlocal diffusion
description We obtain upper bounds for the decay rate for solutions to the nonlocal problem λtu(x, t) = ∫ℝn J(x, y)|u(y, t) - u(x, t)|p-2(u(y, t) - u(x, t)) dy with an initial condition u0 ε L1(ℝn) ∩ L(Rn) and a fixed p > 2. We assume that the kernel J is symmetric, bounded (and therefore there is no regularizing effect) but with polynomial tails, that is, we assume a lower bounds of the form J(x, y) ≥ c1|x - y|-(n+2λ), for |x - y| c2 and J(x, y) . c1, for |x - y| ≤ c2. We prove that (eqution presented) for q ≥ 1 and t large. © 2014 Esteve et al.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
title_short Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
title_full Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
title_fullStr Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
title_full_unstemmed Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
title_sort upper bounds for the decay rate in a nonlocal p-laplacian evolution problem
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16872762_v2014_n_p_Esteve
http://hdl.handle.net/20.500.12110/paper_16872762_v2014_n_p_Esteve
work_keys_str_mv AT rossijuliodaniel upperboundsforthedecayrateinanonlocalplaplacianevolutionproblem
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