Open Access Research

General decay for a system of nonlinear viscoelastic wave equations with weak damping

Baowei Feng1*, Yuming Qin2 and Ming Zhang1

Author Affiliations

1 College of Information Science and Technology, Donghua University, Shanghai, 201620, P.R. China

2 Department of Applied Mathematics, Donghua University, Shanghai, 201620, P.R. China

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Boundary Value Problems 2012, 2012:146  doi:10.1186/1687-2770-2012-146

Published: 13 December 2012

Abstract

In this paper, we are concerned with a system of nonlinear viscoelastic wave equations with initial and Dirichlet boundary conditions in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/146/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/146/mathml/M1">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/146/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/146/mathml/M2">View MathML</a>). Under suitable assumptions, we establish a general decay result by multiplier techniques, which extends some existing results for a single equation to the case of a coupled system.

MSC: 35L05, 35L55, 35L70.

Keywords:
viscoelastic system; general decay; weak damping