Uniform attractors for the non-autonomous reaction-diffusion equations with delays

In this paper, we consider a non-autonomous reaction-diffusion equation with hereditary effects and the nonlinearity f satisfying the polynomial growth of arbitrary p - 1 (p >= 2) order. We employ the asymptotic a priori estimate method (see (J. Differential Equations 223 (2006) 367-399)) to our problem and establish an existence criterion for the (C-L2(Omega), C-Lp(Omega)) - uniform (w.rt sigma is an element of Sigma) attractors (see Theorem 2.18). Then, we obtain the (C-L2(Omega) , C-Lp(Omega)) and (C-L2(Omega) , C-H01(Omega) )-uniform (w.rt sigma is an element of Sigma) attractors by applying the existence criterion and the uniform (w.rt sigma is an element of Sigma) Condition (C) respectively.