Time-dependent global attractor for the wave equation with nonlinear damping in locally uniform space

This paper is dedicated to analyzing the dynamical behavior of the wave equations with nonlinear damping in unbounded domain. First, the well-posedness of the equation is proved in the locally uniform spaces framework. Then, the asymptotical compactness is established by applying the contractive function method. Finally, the existence of $ ({H}_{lu}^1(\mathbb{R}^3) \times{ L}_{lu}^2(\mathbb{R}^3), H_{\rho}^1(\mathbb{R}^3) \times L_{\rho}^2(\mathbb{R}^3)) $-time-dependent global attractor is obtained.