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| Author(s): |
Total Authors: 4
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| Affiliation: | [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
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 41, n. 6, p. 2777-2808, JUN 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 20/04813-0 - Asymptotic and qualitative analysis of integro-differential equations |
| Grantee: | Marcone Corrêa Pereira |
| Support Opportunities: | Regular Research Grants |