### GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE VISCOELASTIC WAVE EQUATION WITH A CONSTANT DELAY TERM

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#### Abstract

In this paper, we investigate the following viscoelastic wave equation with

a constant delay term

\begin{equation*}

u''(x,t)-k_{0}\triangle u +\alpha\int g(t-s)\triangle u(x,s)ds+\mu_{1}(t)u'(x,t)+\mu_{2}(t)u'(x,t-\tau)=0\end{equation*}

in a bounded domain and under suitable assumptions. First, we prove the global

existence by using Faedo-Galerkin procedure. Secondly, the multiplier method is used

to establish a decay estimate for the energy, which depends on the behavior of alpha and g.

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DOI: https://doi.org/10.22190/FUMI1704485R

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