Global attractors of the degenerate fractional Kirchhoff wave equation with structural damping or strong damping

Abstract This article deals with the degenerate fractional Kirchhoff wave equation with structural damping or strong damping. The well-posedness and the existence of global attractor in the natural energy space by virtue of the Faedo-Galerkin method and energy estimates are proved. It is worth mentioning that the results of this article cover the case of possible degeneration (or even negativity) of the stiffness coefficient. Moreover, under further suitable assumptions, the fractal dimension of the global attractor is shown to be infinite by using Z 2 {{\mathbb{Z}}}_{2} index theory.