A new concept called backward controller for an evolution process is introduced, which is the minimal compact set controlling all fibers of the pullback attractor in the past. The existence criteria are established by using the backward flattening compactness and backward equi-continuity of the system if the phase space is all of continuous vector-valued functions. Both backward controller and backward compact attractor are obtained for the non-autonomous Benjamin-Bona-Mahony equation with variable or distributed delay.

中文翻译：

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延迟Benjamin-Bona-Mahony方程的回撤吸引子的后向控制器

引入了一种用于进化过程的称为后向控制器的新概念，该概念是过去控制回拉吸引子的所有纤维的最小紧凑集。如果相空间全部是连续的矢量值函数，则通过使用系统的向后平坦性和向后等连续性来建立存在准则。对于具有可变或分布延迟的非自治Benjamin-Bona-Mahony方程，都获得了向后控制器和向后紧致吸引子。