General decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan–Taylor damping with nonlinear delay and acoustic boundary conditions

Abstract

In this paper, we consider the general decay of solutions for the weak viscoelastic equation of Kirchhoff type containing Balakrishnan–Taylor damping with nonlinear delay and acoustic boundary conditions. By using suitable energy and Lyapunov functionals, we prove the general decay for the energy, which depends on the behavior of both σ and k.

General decay estimate for a viscoelastic wave equation with Balakrishnan-Taylor damping and strong dissipation

“…The presence of delay may be a source of instability. Hence, the problems with the Balakrishnan-Taylor damping in the presence of time delay effects have become one of very interesting topics in recent years, see for instance [9], [10], [11], [15], [16], [17], [19], [22], [23], [24], [38] and the reference therein. In most cases, the interest of this type was contained in studying the following equation…”