Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 405092, 13 pages
doi:10.1155/2008/405092
Research Article

Existence and Uniqueness of Pseudo Almost Automorphic Mild Solutions to Some Classes of Partial Hyperbolic Evolution Equations

Zhanrong Hu1,2 and Zhen Jin1,2

1Department of Mathematics, North University of China, Taiyuan 030051, China
2School of Mechatronic Engineering, North University of China, Taiyuan 030051, China

Received 1 June 2008; Revised 4 July 2008; Accepted 10 September 2008

Academic Editor: Leonid Shaikhet

Copyright © 2008 Zhanrong Hu and Zhen Jin. 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 will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation (d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ, under some assumptions. To illustrate our abstract result, a concrete example is given.