Pullback Attractor For Critical Wave Equation With Time-dependent Damping

This paper is concerned with the long-time dynamics of a non-autonomous wave equation with time-dependent damping,defined in a bounded domain ?(?) R~3 with smooth boundary,the nonlinear term f(u)has a critical growth exponent.Under the hypothesis for the damped coefficient ?(t)which owns positive lower bound,we establish the existence of a pullback D_?-attractor for the process ?(·,·)generated by the solution of(1.1).A contractive function method has been used to deal with the difficulty generated by the critical nonlinearity,which verifies the pullback D_?-asymptotical compactness for ?(·,·).