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2014 Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms
Shuilin Cheng, Yantao Guo, Yanbin Tang
J. Appl. Math. 2014: 1-15 (2014). DOI: 10.1155/2014/450289

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.

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Shuilin Cheng. Yantao Guo. Yanbin Tang. "Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms." J. Appl. Math. 2014 1 - 15, 2014. https://doi.org/10.1155/2014/450289

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010635
MathSciNet: MR3191118
Digital Object Identifier: 10.1155/2014/450289

Rights: Copyright © 2014 Hindawi

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