Abstract and Applied Analysis
Volume 2013 (2013), Article ID 746893, 6 pages
http://dx.doi.org/10.1155/2013/746893
Research Article

Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces

Hongxia Fan,1,2 Yongxiang Li,2 and Pengyu Chen2

1Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
2Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 2 November 2012; Revised 6 January 2013; Accepted 16 January 2013

Academic Editor: Ferenc Hartung

Copyright © 2013 Hongxia Fan et al. 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

This paper deals with the existence and uniqueness of mild solutions for a second order evolution equation initial value problem in a Banach space, which can model an elastic system with structural damping. The discussion is based on the operator semigroups theory and fixed point theorem. In addition, an example is presented to illustrate our theoretical results.