Pullback attractors for a critical degenerate wave equation with time-dependent damping

The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term ∂ttu+β(t)∂tu=Lu(x,t)+f(u) on a bounded domain Ω⊂RN with Dirichlet boundary conditions. Under some restrictions on β(t) and critical growth restrictions on the nonlinear term f, we will prove the local and global well-posedness of the solution and derive the existence of a pullback attractor for the process associated with the degenerate damped hyperbolic problem.