摘要
本文主要研究带记忆项的强阻尼波方程_t^2-△_tu-k(0)△u-∫_0~∞k'(s)△u(t-s)ds+φ(u)=f,解的长时间行为.我们证明了轨道和全局吸引子的存在性,并给出了它们结构的刻画.
In this paper, we study the following strongly damped wave equation with memory effect δt^2u-△δtu-k（0）△u-∫0^∞k＇（s）△u（t-s）ds＋φ（u）=f.Other than consider the problem in the history space setting as the previous works, we are concerned with the corresponding system acts in the space of initial data of the Cauchy problem. We will prove the existence of trajectory attractors and global at- tractors for the above equation. Moreover, we will state the results about the structure for the trajectory and global attractor of the equation.
作者
孟凤娟
刘存才
Meng Fengjuan Liu Cuncai(School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001)
出处
《南京大学学报（数学半年刊）》
2016年第2期114-136,共23页
Journal of Nanjing University(Mathematical Biquarterly)
基金
Supported by the NSFC(11526100)
Natural Science Fund for Colleges and Universities in Jiangsu Province(15KJB110005)
QingLan Project
关键词
轨道吸引子
全局吸引子
波方程
记忆核
trajectory attractor, global attractor, wave equation, memory kernel.
