Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries

Autor(es)

Arrieta, Jose M. ^{[1, 2]} ; Nogueira, Ariadne ^[3] ; Pereira, Marcone C. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal Matemat & Matemat Aplicada, E-28040 Madrid - Spain

^[2] UCM, UC3M, UAM, Inst Ciencias Matemat, CSIC, C Nicolas Cabrera 13-15, Madrid 28049 - Spain

^[3] Univ Sao Paulo, Dept Matemat, IME, Rua Matao 1010, Sao Paulo, SP - Brazil

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

• Tipo de documento: Artigo Científico
• Fonte: COMPUTERS & MATHEMATICS WITH APPLICATIONS; v. 77, n. 2, p. 536-554, JAN 15 2019.
• Citações Web of Science: 2

Resumo

In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the oscillatory boundary. Our main result is concerned with the upper and lower semicontinuity of the set of solutions. We show that the solutions of our perturbed equation can be approximated with one of a one-dimensional equation, which also captures the effects of all relevant physical processes that take place in the original problem. (C) 2018 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 17/02630-2 - Análise assintótica de equações diferenciais e integrais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular