Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614256 | Journal of Mathematical Analysis and Applications | 2016 | 18 Pages |
Abstract
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 ϵ 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Saulo R.M. Barros, Marcone C. Pereira,