Spectral analysis and exponential stability of one-dimensional wave equation with viscoelastic damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Wang, Jing¹  Wang, Jun-Min¹ 

[1] Beijing Inst Technol, Sch Math, Beijing 100081, Peoples R China

关键词: Wave equation;    Viscoelastic damping;    Asymptotic analysis;    Riesz basis;    Stability;   

DOI  :  10.1016/j.jmaa.2013.08.034

来源: Elsevier

【 摘 要 】

This paper presents the exponential stability of a one-dimensional wave equation with viscoelastic damping. Using the asymptotic analysis technique, we prove that the spectrum of the system operator consists of two parts: the point and continuous spectrum. The continuous spectrum is a set of N points which are the limits of the eigenvalues of the system, and the point spectrum is a set of three classes of eigenvalues: one is a subset of N isolated simple points, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum. Moreover, the Riesz basis property of the generalized eigenfunctions of the system is verified. Consequently, the spectrum-determined growth condition holds true and the exponential stability of the system is then established. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free