随机Kuramoto-Sivashinsky格点方程的后向紧随机吸引子  

Backward Compact Random Attractors for Stochastic Kuramoto-Sivashinsky Lattice Equation

作　　者：乔闪闪 李扬荣[1] QIAO Shanshan;LI Yangrong(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第8期48-53,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11571283).

摘　　要：本文主要研究非自治随机Kuramoto-Sivashinsky格点方程.在外力是后向缓增的情况下,首先通过对解的估计,证明了Kuramoto-Sivashinsky格点方程在空间l^(2)上存在随机吸收集,从而推出后向一致吸收集的存在性.其次,证明了格点方程在吸收集上是后向渐近紧的.最后再利用吸引子的存在性定理,证明了非自治随机Kuramoto-Sivashinsky格点方程在空间l^(2)上存在后向紧随机吸引子.It is mainly used to study the non-autonomous random Kuramoto-Sivashinsky lattice equation in the case that the external force is backward slowly increasing.First,by estimating the solution,it is proved that the Kuramoto-Sivashinsky lattice equation has random absorption set on the spacel^(2),then deduce the existence of the backward uniform absorption set.Secondly,it is proved that the lattice equation is asymptotically backward compact on the absorption set.Finally,by means of the existence theorem of the attractor,it is proved that the non-autonomous random Kuramoto-Sivashinsky lattice equation has a backward compact random attractor on the spacel^(2).

关 键 词：Kuramoto-Sivashinsky格点方程 乘性噪音 后向紧随机吸引子 

分 类 号：O193[理学—数学]