Table of Contents
Journal of Difference Equations
Volume 2016, Article ID 3732176, 10 pages
http://dx.doi.org/10.1155/2016/3732176
Research Article

The Exponential Stability Result of an Euler-Bernoulli Beam Equation with Interior Delays and Boundary Damping

Department of Mathematics, Tianjin University, Tianjin 300350, China

Received 20 January 2016; Accepted 9 March 2016

Academic Editor: Honglei Xu

Copyright © 2016 Peng-cheng Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the exponential stability of Euler-Bernoulli beam with interior time delays and boundary damping. At first, we prove the well-posedness of the system by the semigroup theory. Next we study the exponential stability of the system by constructing appropriate Lyapunov functionals. We transform the exponential stability issue into the solvability of inequality equations. By analyzing the relationship between delays parameters and damping parameters , we describe -region for which the system is exponentially stable. Furthermore, we obtain an estimation of the decay rate .