Energy decay of solutions for a wave equation with a constant weak delay and a weak internal feedback - Abbes Benaissa (Electronic Journal of Qualitative Theory of Differential Equations, 2014)
In this paper, we consider the wave equation with a weak internal constant delay term: $$ u''(x, t)-Δ_{x}u(x, t)+ μ_1(t) \ u'(x, t) + μ_2(t) \ u'(x, t-τ) = 0 $$ in a bounded domain. Under appropriate conditions on $μ_1$ and $μ_2$, we prove global existence of solutions by the Faedo-Galerkin method and establish a decay rate estimate for the energy using the multiplier method.