Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 450289, 15 pages
http://dx.doi.org/10.1155/2014/450289
Research Article

Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Received 23 December 2013; Revised 11 February 2014; Accepted 11 February 2014; Published 27 March 2014

Academic Editor: Francisco J. Marcellán

Copyright © 2014 Shuilin Cheng 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

The goal of this paper is to study an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and source terms. Under certain conditions on the initial data: the relaxation function, the indices of nonlinear damping, and source terms and the random force, we prove the local existence and uniqueness of solution by the Galerkin approximation method. Then, considering the relationship between the indices of nonlinear damping and nonlinear source, we give the necessary conditions of global existence and explosion in finite time in some sense of solutions, respectively.