Abstract: We considered the existence of time-dependent global attractors for a class of Kirchhoff-type wave equations with  memory terms, nonlocal strong damping, and nonlinear perturbations. Firstly, we gave the well-posedness result of the solution to the problem. Secondly, we obtained the existence of a pullback absorbing set for the dynamical system in the corresponding solution space by using  energy estimates. Finally, we proved the asymptotic properties  of its process by using the method of contraction functions, thereby the existence of the time-dependent global attractor was established.

Key words:  , Kirchhoff-type wave equation, memory term, nonlocal strong damping, contraction function, time-dependent global attractor