Nonlocal higher order evolution equations

In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the s...

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Autor principal: Rossi, Julio Daniel
Publicado: 2010
Materias:
Asymptotic behaviour
Higher order
Nonlocal diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00036811_v89_n6_p949_Rossi
http://hdl.handle.net/20.500.12110/paper_00036811_v89_n6_p949_Rossi
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00036811_v89_n6_p949_Rossi2023-06-08T14:24:36Z Nonlocal higher order evolution equations Rossi, Julio Daniel Asymptotic behaviour Higher order Nonlocal diffusion In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00036811_v89_n6_p949_Rossi http://hdl.handle.net/20.500.12110/paper_00036811_v89_n6_p949_Rossi
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 behaviour
Higher order
Nonlocal diffusion
spellingShingle Asymptotic behaviour
Higher order
Nonlocal diffusion
Rossi, Julio Daniel
Nonlocal higher order evolution equations
topic_facet Asymptotic behaviour
Higher order
Nonlocal diffusion
description In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Nonlocal higher order evolution equations
title_short Nonlocal higher order evolution equations
title_full Nonlocal higher order evolution equations
title_fullStr Nonlocal higher order evolution equations
title_full_unstemmed Nonlocal higher order evolution equations
title_sort nonlocal higher order evolution equations
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00036811_v89_n6_p949_Rossi
http://hdl.handle.net/20.500.12110/paper_00036811_v89_n6_p949_Rossi
work_keys_str_mv AT rossijuliodaniel nonlocalhigherorderevolutionequations
_version_ 1768542963141443584

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