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 ${\partial }_{tt}u+\beta \left(t\right){\partial }_{t}u=\mathcal{L}u(x,t)+f\left(u\right)$ on a bounded domain $\Omega \subset {\mathbb{R}}^N$ with Dirichlet boundary conditions. Under some restrictions on $\beta \left(t\right)$ 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.

中文翻译：

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具有瞬态阻尼的临界简并波动方程的回拉吸引子

本文的目的是分析具有瞬态阻尼项的简并波动方程解的长期动力学行为。 ${\partial }_{吨吨}你+\beta \left(吨\right){\partial }_{吨}你=\mathcal{升}你(X,吨)+F\left(你\right)$ 在有界域上 $\Omega \subset {\mathbb{电阻}}^N$与 Dirichlet 边界条件。在一些限制下$\beta \left(吨\right)$ 非线性项的临界增长限制 $F$，我们将证明解的局部和全局适定性，并推导出与退化阻尼双曲问题相关的过程的回拉吸引子的存在。