Global existence and maximal attractor of facilitated diffusion model. (English summary) Forum Math. 15 (2003), no. 6, 923–933. The authors study the asymptotic behavior of solutions of a reaction-diffusion system of three equations with non-homogeneous Dirichlet or Robin boundary conditions in a bounded smooth domain of R N. They study the equation in the space of nonnegative functions of (L ∞ (Ω)) 3. They show first the existence of an absorbing set in this space. Afterwards, using the regularization properties of the semigroup, they show that the nonlinear semigroup is asymptotically compact. From here, the existence of the global attractor follows easily
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