具有非线性衰减项的粘弹性波动方程的整体吸引子的存在性  

Existence of the Global Attractor for a Viscoelastic Wave Equation with Nonlinear Damping

作　　者：韩英豪[1] 王儒[1] 胡晓雪[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《吉林师范大学学报（自然科学版）》2013年第1期6-12,共7页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11071106)

摘　　要：设Ω为R3的具有光滑边界的有界区域.考虑了具有非线性衰减项与线性记忆项的半线性波动方程utt+g(ut)-k(0)Δu-∫∞0k'(s)Δu(t-s)ds+f(u)=0,x∈Ω,t∈R+.众所周知,在双曲或双曲类功力系统中非线性衰减性是分析其动力行为的难点所在.在本文我们在能量空间χ0=H10(Ω)×L2(Ω)×M0μ上证明了上述方程的通用吸引子的存在性.Abstract： Let Ω be a bounded domain in R 3 with smooth boundary. We consider the followingsemilinear wave equations with nonlinear damping and linear memory term Uu＋g（ut）-k（0）△u-∫0∞ k＇（s）△u（t-s）ds＋f（u）=0,x∈Ω,t∈R＋. It is well known, that nonlinear disspation in hyperbolic and hyperbolic-like equations has beena source of technical difficulties in the analysis of dynamical systems. In this paper we provethat the existence of the universal attractor for the above equation on the energy space x0=H0 1（Ω）×L2（Ω）×M u 0.

关 键 词：非线性衰减项 半线性波动方程 通用吸引子 

分 类 号：O175.29[理学—数学]