Lamé system with weak damping and nonlinear time-varying delay-Reference-Cited by-同舟云学术

Lamé system with weak damping and nonlinear time-varying delay

Published:2023-01-01 Issue:1 Volume:12 Page:
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Yang Xin-Guang¹,Wang Shubin²,Silva Marcio A. Jorge³

Affiliation:

1. Department of Mathematics and Information Science, Henan Normal University , Xinxiang 453007 , P. R. China

2. School of Mathematics and Statistics, Zhengzhou University , Zhengzhou 450001 , P. R. China

3. Department of Mathematics, State University of Londrina , Londrina 86057-970 , PR , Brazil

Abstract

Abstract This article is concerned with the stability and dynamics for the weak damped Lamé system with nonlinear time-varying delay in a bounded domain. Under some appropriate assumptions, the global well-posedness and asymptotic stability are shown in the case where the delay coefficient is upper dominated by the damping one. Moreover, the finite dimensional global and exponential attractors have also been presented by relying on quasi-stability arguments. The results in this article is an extension of Ma, Mesquita, and Seminario-Huertas’s recent work [Smooth dynamics of weakly damped Lamé systems with delay, SIAM J. Math. Anal. 53 (2021), no. 4, 3759–3771].

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2023-0115/pdf

Reference40 articles.

1. F. Alabau and V. Komornik, Boundary observability, controllability, and stabilization of linear elastodynamic systems, SIAM J. Control Optim. 37 (1999), 521–542.

2. J. Arrieta, A. N. Carvalho and J. K. Hale, A damped hyperbolic equation with critical exponent, Comm. Partial Differential Equations 17 (1992), 841–866.

3. M. Aassila, M. M. Cavalcanti and J. A. Soriano, Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain, SIAM J. Control Optim. 38 (2000), no. 5, 1581–1602.

4. B. F. Apostol, Elastic waves inside and on the surface of a half-space, Quart. J. Mech. Appl. Math. 70 (2017), 289–308.

5. J. M. Ball, Initial boundary value problem for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61–90.