The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging (Q1413028)

The authors study the longtime behavior of solutions of a reaction diffusion system with the nonlinearity rapidly oscillating in time \((f=f(t/\varepsilon,u))\). It is proved that this behavior can be described in terms of global attractors \(A^{\varepsilon}\) of the corresponding dynamical process, and that there attractors tend as \(\varepsilon \rightarrow 0\) to the global attractor \( A^{0}\) of the averaged autonomous system.