Melouka Remil, Ali Hakem

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In this paper, we investigate the following viscoelastic wave equation with
a constant delay term


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

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.


Global existence, energy decay, Faedo-Galerkin method

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