Nonlocal higher order evolution equations

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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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Autores principales: Rossi, J.D., Schönlieb, C.-B.
Formato: JOUR
Materias:
Asymptotic behaviour
Higher order
Nonlocal diffusion
Acceso en línea: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 todo:paper_00036811_v89_n6_p949_Rossi2023-10-03T13:56:31Z Nonlocal higher order evolution equations Rossi, J.D. Schönlieb, C.-B. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, J.D.
Schönlieb, C.-B.
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.
format JOUR
author Rossi, J.D.
Schönlieb, C.-B.
author_facet Rossi, J.D.
Schönlieb, C.-B.
author_sort Rossi, J.D.
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
url http://hdl.handle.net/20.500.12110/paper_00036811_v89_n6_p949_Rossi
work_keys_str_mv AT rossijd nonlocalhigherorderevolutionequations
AT schonliebcb nonlocalhigherorderevolutionequations
_version_ 1807317889685913600

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