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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 L(Ω)(∀q ≥ 2) and H 0 (Ω).

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