Existence and Finite Dimension of a Global Attractor for a Kirchhoff Wave Equation With a Memory Term and a Weak Damping

This paper investigates a Kirchhoff wave equation with a memory term and a weak damping. First, we establish the global well-posedness of the dynamical system using the semigroup method. Next, we apply the energy method to derive a bounded absorbing set and show that the system is asymptotically smooth. Furthermore, we establish a stabilizability like inequality, which leads to the existence of a global attractor with finite fractal and Hausdorff dimensions.