Abstract: We considered  the existence of pullback attractors in non-autonomous wave equations. Firstly, we proved the well-posedness of its solution  according to the uniform sector operator theory. Secondly, the bounded dissipation of the process was obtained by constructing an appropriate functional. Finally, the asymptotic compactness of the process was verified according to the 
operator decomposition technique, and ultimately the existence of the pullback attractor was obtained.  This study not only considers time-dependent damping, but also time-dependent diffusion and time-dependent nonlinear terms. When these time-dependent coefficients meet the appropriate conditions, the existence of the pullback attractor is proven.

Key words: wave equation, well-posedness, pullback attractor, time-dependent coefficient, dissipation, compactness