The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging

The longtime behaviour of solutions of a reaction-diffusion system with the nonlinearity rapidly oscillating in time (f = f(t/ε, u)) is studied. It is proved that (under the natural assumptions) this behaviour can be described in terms of global (uniform) attractors Aε of the corresponding dynamical process and that these attractors tend as ε → 0 to the global attractor A0 of the averaged autonomous system. Moreover, we give a detailed description of the attractors Aε, ε 〈 1, in the case where the averaged system possesses a global Liapunov function