Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
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.
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 decays exponentially. An example is give to illustrate that
the result obtained can be applied to concrete partial differential equations.