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].
Citation
Kaixuan Zhu. Yongqin Xie. Feng Zhou. "$L^{p}$-pullback attractors for non-autonomous reaction-diffusion equations with delays." Topol. Methods Nonlinear Anal. 54 (1) 9 - 27, 2019. https://doi.org/10.12775/TMNA.2019.020