Semilinear elliptic equations in thin domains with reaction terms concentrating on boundary

Autor(es)

Barros, Saulo R. M. ^[1] ; Pereira, Marcone C. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat Aplicada, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 441, n. 1, p. 375-392, SEP 1 2016.
• Citações Web of Science: 5

Resumo

In this paper we analyze the behavior of a family of steady state solutions of a semilinear reaction diffusion equation with homogeneous Neumann boundary condition, posed in a two-dimensional thin domain with reaction terms concentrated in a narrow oscillating neighborhood of the boundary. We assume that the domain, and therefore, the oscillating boundary neighborhood, degenerates into an interval as a small parameter epsilon goes to zero. Our main result is that this family of solutions converges to the solution of a one-dimensional limit equation capturing the geometry and oscillatory behavior of the open sets where the problem is established. (C) 2016 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 13/22275-1 - Sistemas dinâmicos gerados por equações parabólicas semilineares
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular