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

Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory