UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS KIRCHHOFF WAVE EQUATIONS

被引：17
|
作者：
Yang, Zhijian [1 ]
Li, Yanan [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, 100 Sci Rd, Zhengzhou 450001, Henan, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 09期
基金：
中国国家自然科学基金;
关键词：
Non-autonomous Kirchhoff wave equation; structural damping; dissipative index; pullback attractor; upper semicontinuity; EXPONENTIAL ATTRACTORS; LONGTIME DYNAMICS; GLOBAL ATTRACTORS; CONTINUITY; STABILITY; EXISTENCE; PERTURBATION; MODELS; FAMILY;
D O I：
10.3934/dcdsb.2019036
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper investigates the upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with structural damping: u(tt) - M(parallel to del u parallel to(2))Delta u+(-Delta)(alpha)u(t)+f(u) = g(x, t), where alpha is an element of (1/2, 1) is said to be a dissipative index. It shows that when the nonlinearity f(u) is of super-critical growth p : 1 <= p < p(alpha) equivalent to N+4 alpha/(N-4 alpha)(+), the related evolution process has a pullback attractor for each alpha is an element of (1/2, 1), and the family of pullback attractors is upper semicontinuous with respect to alpha. These results extend those in [27] for autonomous Kirchhoff wave models.
引用
收藏
页码：4899 / 4912
页数：14
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