Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 183420, 10 pages
http://dx.doi.org/10.1155/2013/183420
Research Article

Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain

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 5 March 2013; Accepted 22 April 2013

Academic Editor: Yonghui Xia

Copyright © 2013 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

Combining the exponential dichotomy of evolution family, composition theorems for almost automorphic functions with Banach fixed point theorem, we establish new existence and uniqueness theorems for almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain. A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.