AbstractIn this paper, based on the notation of time-dependent attractors introduced by Conti, Pata and Temam in (J.Differ. Equ. 255:1254–1277, 2013), we prove the existence of time-dependent global attractors in $\mathcal{H}_{t}$Ht for a class of nonclassical reaction–diffusion equations with the forcing term $g(x)\in H^{-1}(\varOmega )$g(x)∈H−1(Ω) and the nonlinearity f satisfying the polynomial growth of arbitrary $p-1$p−1 ($p\geq 2$p≥2) order, which generalizes the results obtained in (Appl. Anal. 94:1439–1449, 2015) and (Bound. Val...
