Communications of the
Korean Mathematical Society CKMS

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan--Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with $g$ satisfying some general growth at infinity.

Keywords: Balakrishnan--Taylor damping, general decay rate, time-varying delay, convex function, infinite memory

MSC numbers: Primary 93D15, 74D10, 35L20, 35B40