Pullback Attractors For A Non-autonomous Wave Equation With Critical Nonlinearity And Linear Memory

In this paper,we consider the long-time dynamics of a non-autonomous wave equation with nonlinear interior damping and linear memorywhere u(t)=u(x,t),x??,? is a bounded smooth domain in RN(N?3).The nonlinear term f(u)satisfies the critical growth condition.In this paper,First of all,we proved well-posedness of solution via Faedo-Galerkin approximation method,and then based on the well-posedness of solution,a dynamic system is constructed.Secondly,during proving the nonautonomous dynamic system has the pullback absorb set in the corresponding solution space,we consider the external force g is translation bounded.Finally,we show that it is asymptotically compact via the contractive functions method.Which proved that the existence of the pullback attractor.