带时滞的发展方程时间依赖拉回吸引子的存在性  

Existence of Time-Dependent Pullback Attractor for Evolution Equations with Delay

作　　者：高娟平 刘亭亭 GAO Juanping;LIU Tingting(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第5期1027-1036,共10页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12101502,11961059)。

摘　　要：考虑一类带时滞的非自治二阶发展方程.首先,利用Faedo-Galerkin逼近法得到其在C_(H_(t))上解的存在性和唯一性;其次,借助算子分解验证过程{U(t,τ)}t≥τ在C_(H_(t))上的D_(C_(H_(t)))-拉回渐近紧性,从而证明带时滞的发展方程时间依赖拉回吸引子的存在性.We considered a class of non-autonomous second-order evolution equations with delay.Firstly,we obtained the existence and uniqueness of solution by using Faedo-Galerkin approximation method in C_(H_(t)).Secondly,by means of operator decomposition,the D_(C_(H_(t)))-pullback asymptotic compactness of the process{U(t,τ)}t≥τon C_(H_(t)) was verified,which proved the existence of time-dependent pullback attractor for evolution equations with delay.

关 键 词：发展方程 算子分解 时间依赖拉回吸引子 存在性 

分 类 号：O175.29[理学—数学]