Nonlocal evolution problems in thin domains

In this paper, we consider parabolic nonlocal problems in thin domains. Fix Ω ⊂ RN1 × RN2 and consider uϵ be the solution to (Formula presented.) with initial condition u(0, x) = u0(x) and a kernel of the form Jϵ(x) = J(x1,ϵx2) with J non-singular. This corresponds (via a simple change of variables)...

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Autores principales: Pereira, M.C., Rossi, J.D.
Formato: JOUR
Materias:
45A05
45C05
45M05
asymptotic analysis
Neumann problem
nonlocal equations
Thin domains
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00036811_v97_n12_p2059_Pereira
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00036811_v97_n12_p2059_Pereira
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spelling todo:paper_00036811_v97_n12_p2059_Pereira2023-10-03T13:56:31Z Nonlocal evolution problems in thin domains Pereira, M.C. Rossi, J.D. 45A05 45C05 45M05 asymptotic analysis Neumann problem nonlocal equations Thin domains In this paper, we consider parabolic nonlocal problems in thin domains. Fix Ω ⊂ RN1 × RN2 and consider uϵ be the solution to (Formula presented.) with initial condition u(0, x) = u0(x) and a kernel of the form Jϵ(x) = J(x1,ϵx2) with J non-singular. This corresponds (via a simple change of variables) to the usual nonlocal evolution problem (Formula presented.), in the thin domain (Formula presented.). Our main result says that there is a limit as (Formula presented.) of the solutions to our problem and that this limit, when we take its mean value in the (Formula presented.) -direction, is a solution to a limit nonlocal problem in the projected set Ω1 ⊂ RN1. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group. 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_v97_n12_p2059_Pereira
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 45A05
45C05
45M05
asymptotic analysis
Neumann problem
nonlocal equations
Thin domains
spellingShingle 45A05
45C05
45M05
asymptotic analysis
Neumann problem
nonlocal equations
Thin domains
Pereira, M.C.
Rossi, J.D.
Nonlocal evolution problems in thin domains
topic_facet 45A05
45C05
45M05
asymptotic analysis
Neumann problem
nonlocal equations
Thin domains
description In this paper, we consider parabolic nonlocal problems in thin domains. Fix Ω ⊂ RN1 × RN2 and consider uϵ be the solution to (Formula presented.) with initial condition u(0, x) = u0(x) and a kernel of the form Jϵ(x) = J(x1,ϵx2) with J non-singular. This corresponds (via a simple change of variables) to the usual nonlocal evolution problem (Formula presented.), in the thin domain (Formula presented.). Our main result says that there is a limit as (Formula presented.) of the solutions to our problem and that this limit, when we take its mean value in the (Formula presented.) -direction, is a solution to a limit nonlocal problem in the projected set Ω1 ⊂ RN1. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.
format JOUR
author Pereira, M.C.
Rossi, J.D.
author_facet Pereira, M.C.
Rossi, J.D.
author_sort Pereira, M.C.
title Nonlocal evolution problems in thin domains
title_short Nonlocal evolution problems in thin domains
title_full Nonlocal evolution problems in thin domains
title_fullStr Nonlocal evolution problems in thin domains
title_full_unstemmed Nonlocal evolution problems in thin domains
title_sort nonlocal evolution problems in thin domains
url http://hdl.handle.net/20.500.12110/paper_00036811_v97_n12_p2059_Pereira
work_keys_str_mv AT pereiramc nonlocalevolutionproblemsinthindomains
AT rossijd nonlocalevolutionproblemsinthindomains
_version_ 1807318096045670400

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