UNIFORM ATTRACTOR AND ITS KOLMOGOROV ENTROPY FOR A DAMPED SUP-CUBIC WAVE EQUATION WITH STATE-DEPENDENT DELAY

被引：0
作者：
Xiong, Yangmin [1 ]
Mei, Xinyu [2 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
[2] Yunnan Univ, Sch Math & Stat, Kunming 650091, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 12期
关键词：
Wave equation; uniform attractor; Strichartz estimate; state-dependent delay; Kolmogorov's entropy; DIFFERENTIAL-EQUATIONS; EVOLUTION-EQUATIONS; 2ND-ORDER;
D O I：
10.3934/cpaa.2023115
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The well-posedness and asymptotic dynamics of non-autonomous wave equations with state-dependent delay and sup-cubic nonlinearity are investigated. Based on the Strichartz estimates, we first obtain the wellposedness in a C1-type space. Then, we present a general scheme for considering the dynamics, which generalizes the method of quasi-stability to the non-autonomous setting. Applying this scheme to our concrete model, we establish the existence of a uniform attractor and give its entropy estimates.
引用
收藏
页码：3343 / 3362
页数：20
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