Attractors of some reaction diffusion problems

In this paper we study the existence and stability properties of certain so lutions of a semilinear parabolic equation with Robin boundary conditions. We are actually interested in solutions that exhibit both boundary and inte rnal layers. We give an extension of the Sturm-Liouville theory to treat th is problem and compute the number of stable solutions. We also completely d etermine the attractor for a few examples. Finally, we show that our result s are robust and that, in particular, the structure of these attractors per sist under small perturbations.