In this talk we discuss the behavior of a family of steady state solutions
of a semi-linear reaction-diffusion equation with homogeneous Neumann
boundary condition posed in a two-dimensional thin domain when some
reaction terms of the problem are concentrated in a narrow oscillating
neighborhood of the boundary. We assume that the domain, and so, the
oscillating neighborhood, degenerates to an interval as a small parameter
goes to zero. Our main goal here is to show that this family of solutions
converges to the solutions of an one-dimensional limit equation capturing
the geometry and oscillatory behavior of the open sets where the problem is
established adapting methods and techniques developed in [1, 2, 3] and [4].