PULLBACK EXPONENTIAL ATTRACTORS FOR NONAUTONOMOUS DYNAMICAL SYSTEM IN SPACE OF HIGHER REGULARITY

Abstract

Under what condition, a process which exists a (E, E)-pullback exponential attractor implies the existence of (E, V)-pullback exponential attractor when V embedded in E? We answer this question in this paper. As an application of this result, we prove the existence of pullback exponential attractor for a nonlinear reaction-diffusion equation with a polynomial growth nonlinearity in Lq(Ω)(∀q ≥ 2) and H01(Ω).