Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term

Abstract

In this paper, we present an analysis of stability of solutions corresponding to a variable coefficient's wave equation subject to a locally Kelvin–Voigt damping and distributed effect driven by a nonnegative function with dynamic Wentzell boundary conditions and delay term. By using frequency domain approach method, we show that under a suitable assumption between the internal damping function and the boundary delay feedback, considering some geometrical assumptions on the boundary of , supposing that the relaxation function decay exponentially to zero, that the energies of the problem decay exponentially to zero.