The Exponential Stability Result of an Euler-Bernoulli Beam Equation with Interior Delays and Boundary Damping. (31st May 2016)

• Record Type: Journal Article
• Authors: Han, Peng-cheng; Li, Yan-fang; Xu, Gen-qi; Liu, Dan-hong
• Other Names: Xu Honglei Academic Editor.
• Is Part Of: Journal of difference equations. Volume 2016(2016)
• Publication Date: 2016-05-31
• Subjects: Difference equations -- Periodicals; Difference equations; Periodicals; 515.625
• DOI: 10.1155/2016/3732176
• Languages: English
• ISSNs: 2356-7856

Abstract

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 theC 0 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 parametersα and damping parametersβ, we describe( β, α ) -region for which the system is exponentially stable. Furthermore, we obtain an estimation of the decay rateλ ⁎ .