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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todo:paper_16872762_v2014_n_p_Esteve2023-10-03T16:29:51Z Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem Esteve, C. Rossi, J.D. Antolin, A.S. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Esteve, C. Rossi, J.D. Antolin, A.S. 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. |
| format |
JOUR |
| author |
Esteve, C. Rossi, J.D. Antolin, A.S. |
| author_facet |
Esteve, C. Rossi, J.D. Antolin, A.S. |
| author_sort |
Esteve, C. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_16872762_v2014_n_p_Esteve |
| work_keys_str_mv |
AT estevec upperboundsforthedecayrateinanonlocalplaplacianevolutionproblem AT rossijd upperboundsforthedecayrateinanonlocalplaplacianevolutionproblem AT antolinas upperboundsforthedecayrateinanonlocalplaplacianevolutionproblem |
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1807323668452212736 |