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The aim of this paper is to analyze the long-time dynamical behavior of thesolution for a degenerate wave equation with time-dependent damping term$\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a boundeddomain $\Omega\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Undersome restrictions on $\beta(t)$ and critical growth restrictions on thenonlinear term $f$, we will prove the local and global well-posedness of thesolution and derive the existence of a pullback attractor for the processassociated with the degenerate damped hyperbolic problem.

Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping