HOMOGENIZATION FOR NONLOCAL PROBLEMS WITH SMOOTH KERNELS

Autor(es)

Capanna, Monia ^{[1, 2]} ; Nakasato, Jean C. ^[3] ; Pereira, Marcone C. ^[4] ; Rossi, Julio D. ^{[1, 2]}

Afiliação do(s) autor(es)

^[1] Univ Buenos Aires, CONICET, Ciudad Univ, Pabellon 1, RA-1428 Buenos Aires, DF - Argentina

^[2] Univ Buenos Aires, Dept Matemat, FCEyN, Ciudad Univ, Pabellon 1, RA-1428 Buenos Aires, DF - Argentina

^[3] Univ Sao Paulo, Dept Matemat, ICMC, Ave Trabalhador Sao Carlense 400, Sao Carlos, SP - Brazil

^[4] Univ Sao Paulo, Dept Matemat Aplicada, IME, Rua Matao 1010, Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 41, n. 6, p. 2777-2808, JUN 2021.
• Citações Web of Science: 0

Resumo

In this paper we consider the homogenization problem for a nonlocal equation that involve different smooth kernels. We assume that the spacial domain is divided into a sequence of two subdomains A(n) boolean OR B-n and we have three different smooth kernels, one that controls the jumps from A(n) to A(n), a second one that controls the jumps from B-n to B-n and the third one that governs the interactions between A(n) and B-n. Assuming that chi(An) (x) -> X(x) weakly-{*} in L-infinity (and then chi(Bn) (x) -> (1 - X)(x) weakly-{*} in L-infinity) as n -> 1 we show that there is an homogenized limit system in which the three kernels and the limit function X appear. We deal with both Neumann and Dirichlet boundary conditions. Moreover, we also provide a probabilistic interpretation of our results. (AU)

• Processo FAPESP: 20/04813-0 - Análise assintótica e qualitativa de equações integro-diferenciais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular