Energy decay of solutions for a wave equation with a constant weak delay and a weak internal feedback

摘要

In this paper, we consider the wave equation with a weak internal constant delay term: $$ u''(x, t)-Delta_{x}u(x, t)+ mu_1(t) u'(x, t) + mu_2(t) u'(x, t-au) = 0 $$ in a bounded domain. Under appropriate conditions on $mu_1$ and $mu_2$, we prove global existence of solutions by the Faedo-Galerkin method and establish a decay rate estimate for the energy using the multiplier method.