$L^{p}$-pullback attractors for non-autonomous reaction-diffusion equations with delays

Abstract

In this paper, we consider the non-autonomous reaction-diffusion equations with hereditary effects and the nonlinear term $f$ satisfying the polynomial growth of arbitrary order $p-1$ $(p\geq2)$. The delay term may be driven by a function with very weak assumptions, namely, just measurability. We extend the asymptotic a priori estimate method (see [29]) to our problem and establish a new existence theorem for the pullback attractors in $C_{L^{p}(\Omega)}$ $(p> 2)$ (see Theorem 2.12), which generalizes the results obtained in [12].