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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Barros, Saulo R. M.¹  Pereira, Marcone C.¹ 

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

关键词: Semilinear elliptic equations;    Singular elliptic equations;    Upper semicontinuity;    Lower semicontinuity;    Thin domains;    Concentrating terms;   

DOI  :  10.1016/j.jmaa.2016.04.011

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free