In 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 $\mathcal{H}_{t}$ for a class of nonclassical reaction–diffusion equations with the forcing term $g(x)\in H^{-1}(\varOmega )$ and the nonlinearity f satisfying the polynomial growth of arbitrary $p-1$ ($p\geq 2$) order, which generalizes the results obtained in (Appl. Anal. 94:1439–1449, 2015) and (Bound. Value Probl. 2016: 10, 2016).

中文翻译：

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时变空间上非经典反应扩散方程的吸引子

在本文中，基于Conti，Pata和Temam在（J. Differ。Equ。255：1254-1277，2013）中引入的时变吸引子的概念，我们证明了$ \中存在时变全局吸引子一类非经典反应扩散方程，其强迫项为：$ g（x）\ in H ^ {-1}（\ varOmega）$，并且非线性f满足任意多项式增长的要求，则为mathcal {H} _ {t} $ $ p-1 $（$ p \ geq 2 $）订单，将（Appl。Anal。94：1439-1449，2015）和（Bound。Value Probl。2016：10，2016）中获得的结果进行概括。