Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-30 DOI:10.57262/ade028-0708-685

E. Tavares, M. A. J. Silva, V. Narciso, A. Vicente

引用次数: 2

Abstract

This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the results feature the existence of a family of compact global attractors and a thickness estimate for their Kolmogorov's $\varepsilon$-entropy. Then, in the non-degenerate context, the structure of the helpful nonlocal damping leads to the existence of finite-dimensional compact global and exponential attractors. Lastly, in a degenerate and critical framework, it is proved the existence of a bounded closed global attractor but not compact. To the proofs, we provide several new technical results by means of refined estimates that open up perspectives for a new branch of nonlinearly damped problems.

查看原文本刊更多论文

一类具有简并和非简并非局部阻尼的可扩展梁的动力学

本文研究了一类与具有三个不同非局部非线性阻尼项的可伸展梁相关的双曲型发展方程的长期动力学的新结果。在第一个可能退化的情况下，结果表明存在一个紧致全局吸引子族，并对其Kolmogorov的$\varepsilon$-熵进行了厚度估计。然后，在非退化情况下，有用的非局部阻尼的结构导致有限维紧致全局和指数吸引子的存在。最后，在一个退化的临界框架中，证明了有界闭全局吸引子的存在性，但它不是紧致的。对于这些证明，我们通过精细估计提供了一些新的技术结果，为非线性阻尼问题的一个新分支开辟了前景。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.