Semigroup well-posedness and exponential stability for the von Kármán beam equation under the combined boundary control of nonlinear delays and non-delays

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-31 DOI:10.1016/j.nonrwa.2024.104143

Yi Cheng , Xin Wang , Baowei Feng , Donal O’ Regan

引用次数: 0

Abstract

This paper considers the stabilization problem of the von Kármán beam equation with a combined boundary control of nonlinear delays and nonlinear non-delays. The combined boundary controls are applied at the transverse and longitudinal boundaries of the von Kármán beam, respectively. In this paper the nonlinear semigroup method is adopted in the investigation for the establishment of the well-posedness of the resulting closed-loop system. Constructing an appropriate energy-like function, the exponential decay rate of energy of the closed-loop system is demonstrated by a generalized Gronwall-type integral inequality and the integral multiplier technique.

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非线性延迟和非延迟联合边界控制下 von Kármán 梁方程的半群好求和指数稳定性

本文研究了具有非线性延迟和非线性非延迟组合边界控制的 von Kármán 梁方程的稳定问题。组合边界控制分别应用于 von Kármán 梁的横向和纵向边界。本文在研究中采用了非线性半群法，以建立闭环系统的良好拟合。通过构造一个适当的类能量函数，利用广义格伦沃尔积分不等式和积分乘法器技术证明了闭环系统能量的指数衰减率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.