A Semilinear Reaction–Diffusion System of Equations and Large Diffusion

The long time dynamics for a semilinear system of reaction and diffusion equations with nonlinear boundary conditions in which large diffusion is assumed on all parts of the domain is studied. We show in both local and global dynamics of the system that flows on attractors are essentially close to the ones of a finite dimensional system of equations, which turn out to be the natural limit of the process for large diffusivity.