Attractors for the degenerate Kirchhoff wave model with strong damping: Existence and the fractal dimension

Abstract In this paper, we study the long time behavior of the Kirchhoff type wave equation in the space H 0 1 ( Ω ) × L 2 ( Ω ) . We prove the existence of the global attractor for the equation which covers the case of possible generation of the stiffness coefficient. We also consider the geometrical property of the global attractor. By means of the Z 2 index, we provide, under suitable assumptions, the fractal dimension of the global attractor is infinite.