  This paper is concerned with the existence and regularity of global attractor
$\mathcal A$ for a Kirchhoff wave equation with strong damping and memory in
the weighted time-dependent spaces $\mathcal H$ and $\mathcal H^{1}$,
respectively. In order to obtain the existence of $\mathcal A$, we mainly use
the energy method in the priori estimations, and then verify the asymptotic
compactness of the semigroup by the method of contraction function. Finally, by
decomposing the weak solutions into two parts and some elaborate calculations,
we prove the regularity of $\mathcal A$.

Analysis of PDEs;Dynamical Systems