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

Abstract

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 L 2 ( Ω ) , C L p ( Ω ) )-uniform (w.r.t σ ∈ Σ) attractors (see Theorem 2.18). Then, we obtain the ( C L 2 ( Ω ) , C L p ( Ω ) ) and ( C L 2 ( Ω ) , C H 0 1 ( Ω ) )-uniform (w.r.t σ ∈ Σ) attractors by applying the existence criterion and the uniform (w.r.t σ ∈ Σ) Condition (C) respectively.