带时滞项的高阶Kirchhoff型方程的惯性流形  

Inertial manifolds for the higher-order Kirchhoff-type equation with the time delay

作　　者：王利波 徐瑰瑰 林国广[2] WANG Libo;XU Guigui;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,贵州凯里556011 [2]云南大学数学与统计学院,云南昆明650091

出　　处：《安徽大学学报（自然科学版）》2021年第4期8-16,共9页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11561076);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]328);贵州省科技厅科学技术联合基金资助项目(黔科合LH[2017]7165)。

摘　　要：研究带时滞项的高阶Kirchhoff型方程.利用Fadeo-Galerkin方法和经典的不动点理论,证明了解的存在性和唯一性;在一定的谱间隔条件和充分小的时滞假设下,利用算子半群理论及Lyapunov-Perron方法证明了惯性流形的存在性.The higher-order Kirchhoff-type equation with time delay was discussed.By using the Fadeo-Galerkin method and the classical fixed point theory,the existence and uniqueness of solution was yielded.By using semigroup of operator theory and Lyapunov-perron method in the assumptions of spectral gap condition and sufficiently small retarded time,the existence of the inertial manifolds was obtained.

关 键 词：时滞 Fadeo-Galerkin方法 谱间隔条件 惯性流形 

分 类 号：O175.29[理学—数学]