Communications in Mathematical Sciences

Volume 21 (2023)

Number 5

Existence of polynomial attractor for a class of extensible beams with nonlocal weak damping

Pages: 1393 – 1413

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n5.a10

Authors

Chunxiang Zhao (Institute of Applied System Analysis, Jiangsu University, Zhenjiang, China)

Chunyan Zhao (School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, China)

Chengkui Zhong (Department of Mathematics, Nanjing University, Nanjing, China)

Abstract

In this paper, we put forward the concept of polynomial attractor and study the connection between the polynomial attractors and the estimate of attractive velocity of bounded sets for infinite-dimensional dynamical systems. Then we prove the existence of polynomial attractor for a class of extensible beams with nonlocal weak damping for the case that the nonlinear term $f$ has subcritical growth.

Keywords

polynomial attractor, attractive velocity, the polynomial decay, extensible beams, nonlocal weak damping

2010 Mathematics Subject Classification

35B40, 35B41, 37B55

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Received 23 June 2021

Accepted 26 October 2022

Published 30 August 2023