TITLE:
Stable boundary layers in a diffusion problem with
nonlinear reaction at the boundary

AUTHORS:
Jos{\'e} M. Arrieta, Neus C{\'o}nsul and An{\'\i}bal Rodr{\'\i}guez-Bernal

ABSTRACT:
We prove the existence of nonconstant stable stationary solutions
of an evolution problem with a nonlinear reaction acting on the
boundary. These solutions present layers at certain points of the
boundary. We also study the behavior of these solutions as the small
parameter appearing in the equation approaches zero and show some
stability properties of the profiles given by these equilibrium
solutions.

2000 Mathematics Subject Classification:
Primary 37L15; Secondary 35K57

Keywords:
boundary reaction, patterns, boundary layers, energy, minimizers, stability