  In this paper, we shall investigate the existence and upper semicontinuity of
pullback attractors for non-autonomous Kirchhoff wave equations with a strong
damping in the time-dependent space $X_t$. After deriving the existence and
uniqueness of solutions by the Faedo-Galerkin approximation method, we
establish the existence of pullback attractors. Later on, we prove the upper
semicontinuity of pullback attractors between the Kirchhoff-type wave equations
with $\delta \geq 0$ and the conventional wave equations with $\delta=0$ by a
series of complex energy estimates.
