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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.


Documento: Artículo
Título:Nonlocal evolution problems in thin domains
Autor:Pereira, M.C.; Rossi, J.D.
Filiación:Dpto. de Matemática Aplicada, IME, Universidade de São Paulo, São Paulo, Brazil
Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:45A05; 45C05; 45M05; asymptotic analysis; Neumann problem; nonlocal equations; Thin domains
Página de inicio:2059
Página de fin:2070
Título revista:Applicable Analysis
Título revista abreviado:Appl. Anal.


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---------- APA ----------
Pereira, M.C. & Rossi, J.D. (2018) . Nonlocal evolution problems in thin domains. Applicable Analysis, 97(12), 2059-2070.
---------- CHICAGO ----------
Pereira, M.C., Rossi, J.D. "Nonlocal evolution problems in thin domains" . Applicable Analysis 97, no. 12 (2018) : 2059-2070.
---------- MLA ----------
Pereira, M.C., Rossi, J.D. "Nonlocal evolution problems in thin domains" . Applicable Analysis, vol. 97, no. 12, 2018, pp. 2059-2070.
---------- VANCOUVER ----------
Pereira, M.C., Rossi, J.D. Nonlocal evolution problems in thin domains. Appl. Anal. 2018;97(12):2059-2070.