Jk. Hale et G. Raugel, A REACTION-DIFFUSION EQUATION ON A THIN L-SHAPED DOMAIN, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 125, 1995, pp. 283-327
We consider a dissipative reaction-diffusion equation on a thin L-shap
ed domain (with the thinness measured by a parameter a); we determine
the limit equation for epsilon = O and prove the upper semicontinuity
of the global attractors at epsilon = O. We also state a lower semicon
tinuity result. When the limit equation is one-dimensional, we prove c
onvergence of any orbit to a singleton.