具有状态相关延迟的阻尼超三次波动方程的一致吸引子及其Kolmogorov熵

IF 1 3区数学 Q1 MATHEMATICS

Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI:10.3934/cpaa.2023115

Yangmin Xiong, Xinyu Mei

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引用次数: 0

摘要

研究了具有状态相关时滞和超三次非线性的非自治波动方程的适定性和渐近动力学问题。基于Strichartz估计，我们首先得到了C^1 $型空间中的适定性。然后，我们给出了考虑动力学的一般方案，将拟稳定方法推广到非自治设置。将此格式应用到我们的具体模型中，我们建立了一致吸引子的存在性，并给出了它的熵估计。

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Uniform attractor and its Kolmogorov entropy for a damped sup-cubic wave equation with state-dependent delay

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 well-posedness in a $ C^1 $-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.

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来源期刊

Communications on Pure and Applied Analysis 数学-数学

CiteScore

1.90

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.