带时滞项的Boussinesq-Beam方程的拉回吸引子  

Pullback Attractors for the Boussinesq-Beam Equation with Time Delay

作　　者：徐瑰瑰 王利波 林国广[2] XU Guigui;WANG Libo;LIN Guoguang(School of Science,Kaili University,Kaili 556011,China;School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)

机构地区：[1]凯里学院理学院,凯里556011 [2]云南大学数学与统计学院,昆明650091

出　　处：《华南师范大学学报（自然科学版）》2020年第1期104-111,共8页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11561076);贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]306)

摘　　要：利用压缩函数的方法和相关理论,研究带时滞项的Boussinesq-Beam方程的拉回吸引子的存在性:首先通过作内积和不等式估计得到拉回吸收集的存在性,然后借助构造具体的能量泛函并结合收缩函数法的思想验证带时滞项的Boussinesq-Beam方程的解所生成的过程{U(t,τ)}t≥τ在C D(A),V中是渐近紧的,最后证明过程{U(t,τ)}t≥τ在C D(A),V中存在拉回吸引子.The existence of pullback attractors for the Boussinesq-Beam equation with time delay is handled with the concept of contractive function and some related method.Firstly,the existence of a pullback absorbing set is verified by taking the inner product and estimating the inequalities.Then the specific energy function is constructed and the method of contractive functions is used to prove that the process{U(t,τ)}t≥τ in C D(A),V produced by the Boussinesq-Beam equation with time delay possess compactness.Finally,the existence of pullback attractors in C D(A),V for the process{U(t,τ)}t≥τis proved.

关 键 词：时滞 拉回吸收集 紧性 拉回吸引子 

分 类 号：O175.29[理学—数学]