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

Melouka Remil, Ali Hakem
2017 NIŠNIˇNIŠ) Ser. Math. Inform   unpublished
In this paper, we investigate the following viscoelastic wave equation with a constant delay term u ′′ (x, t) − k0△u + α t 0 g(t − s)△u(x, s)ds + µ1(t)u ′ (x, t) + µ2(t)u ′ (x, t − τ) = 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 α and g.
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