GENERAL STABILITY FOR THE VISCOELASTIC WAVE EQUATION WITH NONLINEAR
DAMPING AND NONLINEAR TIME-VARYING DELAY AND ACOUSTIC BOUNDARY
CONDITIONS
Abstract
In this paper, we are concerned with the energy decay rates for the
viscoelastic wave equation with nonlinear damping and nonlinear
time-varying delay in the boundary and acoustic boundary conditions.
Here we consider with minimal condition on the relaxation function
g, namely g ′ ( t ) ≤ − µ ( t ) G ( g ( t ) ) , where G is
an increasing and convex function near the origin and µ is a
positive nonincreasing function. The decay rates of the energy depend on
the functions µ,G and on the function F defined by f 0
which represents the growth at the origin of