乘法噪音下Kuramoto-Sivashinsky方程的后向紧随机奇拉回吸引子  

The Backward Compact Random Odd Pullback Attractor of The Kuramoto-Sivashinsky Equation Under Multiplicative Noise

作　　者：夏欢 李扬荣[1] XIA Huan;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）》2023年第5期22-29,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12271444).

摘　　要：在由奇函数构成的勒贝格空间上研究了带有彩色系数和乘法噪音的随机Kuramoto-Sivashinsky方程对应解的长时间动力行为.在外力是后向缓增的假设下,利用桥函数和彩色噪音的性质对方程的解进行了后向一致估计,由此构造一个后向一致吸收集,并证明了协循环的后向渐近紧性.最后利用吸引子的存在性定理证明了后向紧奇拉回吸引子的存在性及其可测性.In this paper,we study the long-time dynamic behavior for the solution of stochastic Kuramoto-Sivashinsky equation with color coefficient and multiplicative noise on a Lebesgue space composed of odd functions.Under the assumption that the external force is backward tempered,we obtain the backward-uniform estimates of the solution by using the properties of bridge function and color noise.Thus a backward-uniform absorption set is constructed and the backward asymptotic compactness of cocycle is proved.Finally,the existence and measurability of the backward compact odd pullback attractor are proved by using the existence theorem of attractors.

关 键 词：KURAMOTO-SIVASHINSKY方程 乘法噪音 后向紧随机拉回吸引子 

分 类 号：O193[理学—数学]