Refined asymptotic expansions for nonlocal diffusion equations

We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u t = J*u - u in the whole ℝ with an initial condition u(x, 0) = u 0(x). Under suitable hypotheses on J (involving its Fourier transform) and u 0, it is proved an expansion of the form equation is presented where...

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Autor principal: Rossi, Julio Daniel
Publicado: 2008
Materias:
Asymptotic behavior
Fractional Laplacian
Nonlocal diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n4_p617_Ignat
http://hdl.handle.net/20.500.12110/paper_14243199_v8_n4_p617_Ignat
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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_14243199_v8_n4_p617_Ignat2023-06-08T16:13:50Z Refined asymptotic expansions for nonlocal diffusion equations Rossi, Julio Daniel Asymptotic behavior Fractional Laplacian Nonlocal diffusion We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u t = J*u - u in the whole ℝ with an initial condition u(x, 0) = u 0(x). Under suitable hypotheses on J (involving its Fourier transform) and u 0, it is proved an expansion of the form equation is presented where K t is the regular part of the fundamental solution and the exponent A depends on J, q, k and the dimension d. Moreover, we can obtain bounds for the difference between the terms in this expansion and the corresponding ones for the expansion of the evolution given by fractional powers of the Laplacian, ν-t (x, t) = -(-Δ) 2ν (x, t). © 2008 Birkhaueser. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n4_p617_Ignat http://hdl.handle.net/20.500.12110/paper_14243199_v8_n4_p617_Ignat
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic behavior
Fractional Laplacian
Nonlocal diffusion
spellingShingle Asymptotic behavior
Fractional Laplacian
Nonlocal diffusion
Rossi, Julio Daniel
Refined asymptotic expansions for nonlocal diffusion equations
topic_facet Asymptotic behavior
Fractional Laplacian
Nonlocal diffusion
description We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u t = J*u - u in the whole ℝ with an initial condition u(x, 0) = u 0(x). Under suitable hypotheses on J (involving its Fourier transform) and u 0, it is proved an expansion of the form equation is presented where K t is the regular part of the fundamental solution and the exponent A depends on J, q, k and the dimension d. Moreover, we can obtain bounds for the difference between the terms in this expansion and the corresponding ones for the expansion of the evolution given by fractional powers of the Laplacian, ν-t (x, t) = -(-Δ) 2ν (x, t). © 2008 Birkhaueser.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Refined asymptotic expansions for nonlocal diffusion equations
title_short Refined asymptotic expansions for nonlocal diffusion equations
title_full Refined asymptotic expansions for nonlocal diffusion equations
title_fullStr Refined asymptotic expansions for nonlocal diffusion equations
title_full_unstemmed Refined asymptotic expansions for nonlocal diffusion equations
title_sort refined asymptotic expansions for nonlocal diffusion equations
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n4_p617_Ignat
http://hdl.handle.net/20.500.12110/paper_14243199_v8_n4_p617_Ignat
work_keys_str_mv AT rossijuliodaniel refinedasymptoticexpansionsfornonlocaldiffusionequations
_version_ 1768542753717747712

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