Advances in Difference Equations
Volume 2011 (2011), Article ID 879649, 14 pages
doi:10.1155/2011/879649
Research Article

Exponential Stability of Two Coupled Second-Order Evolution Equations

Qian Wan and Ti-Jun Xiao

Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 30 October 2010; Accepted 21 November 2010

Academic Editor: Toka Diagana

Copyright © 2011 Qian Wan and Ti-Jun Xiao. 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

By using the multiplier technique, we prove that the energy of a system of two coupled second order evolution equations (one is an integro-differential equation) decays exponentially if the convolution kernel 𝑘 decays exponentially. An example is give to illustrate that the result obtained can be applied to concrete partial differential equations.