Pullback exponential attractors for nonautonomous equations Part II: Applications to reaction–diffusion systems

Abstract

The existence of a pullback exponential attractor being a family of compact and positively invariant sets with a uniform bound on their fractal dimension which at a uniform exponential rate pullback attract bounded subsets of the phase space under the evolution process is proved for the nonautonomous logistic equation and a system of reaction–diffusion equations with time-dependent external forces including the case of the FitzHugh–Nagumo system.