A new scenario for stability of nonlinear Bresse‐Timoshenko type systems with time dependent delay,ZAMM - Journal of Applied Mathematics and Mechanics

当前位置： X-MOL 学术 › ZAMM › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

A new scenario for stability of nonlinear Bresse‐Timoshenko type systems with time dependent delay
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2019-12-23 , DOI: 10.1002/zamm.201900160
B. Feng ₁ , D. S. Almeida ₂ , M. J. Santos ₃ , L. G. Rosário Miranda ₂

Affiliation

In this paper, we study the asymptotic behavior for a Bresse‐Timoshenko type system with time‐dependent delay terms. Our results follow a recent approach given by Almeida Júnior and Ramos (Zeitschrift f

\ddot{u}

r angewandte Mathematik und Physik. 68, 1‐31. 2017) where they showed that the viscous damping acting on angle rotation of the classical Bresse‐Timoshenko model eliminates the damage consequences of the so called second spectrum of frequency. Moreover, for Bresse‐Timoshenko type systems which are free of these consequences the assumption of equal wave speeds is not necessary anymore to get the exponential stability. Here, by introducing an appropriate Lyapunov functional we prove the exponential stability for time dependent delay cases regardless of any relationship between wave propagation velocities.

中文翻译：

具有时滞的非线性Bresse‐Timoshenko型系统稳定性的新情形

在本文中，我们研究了具有时滞项的Bresse‐Timoshenko型系统的渐近行为。我们的结果遵循AlmeidaJúnior和Ramos（Zeitschrift f

\ddot{ü}

朗诵数学和物理。68，1-31。2017年），他们表明粘性阻尼作用于经典的Bresse‐Timoshenko模型的角旋转，消除了所谓的第二频谱频谱的损害后果。而且，对于没有这些后果的Bresse‐Timoshenko型系统，不再需要相等的波速来获得指数稳定性。在这里，通过引入适当的Lyapunov函数，我们证明了与时间相关的时滞情况的指数稳定性，而与波传播速度之间的任何关系无关。

更新日期：2019-12-23

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文