GLOBAL EXISTENCE AND STABILITY OF SOLUTION FOR A WAVE EQUATION WITH A CONSTANT DELAY AND A WEAK INTERNAL FEEDBACK
REMIL MELOUKA *
Ahmed Zabana university, 48000 Relizane, Algeria.
BENYAMINA HAYET
Ahmed Zabana university, 48000 Relizane, Algeria.
ZERIGUE SORAYA
Ahmed Zabana university, 48000 Relizane, Algeria.
*Author to whom correspondence should be addressed.
Abstract
In this work, we study the following wave equation with a constant weak delay
utt(x,t)- Δu(x,t) - Δutt(x,t) + μ1(t)μt (x,t) + u2(t)μt (x,t - τ)=0
in a bounded domain and under some assumptions. First, we prove the global existence by using Faedo-Galerkin procedure and uniqueness. Secondly, the multiplier method is used to establish the stability of solution.
Keywords: Energy decay, viscoelastic, Faedo-Galerkin, multiplier method