Pullback Attractors For Non-autonomous Wave Equations With State-dependent Delay And Critical Nonlinearity

In this paper,we consider the long-time behavior of the following nonautonomous weakly damped wave equation with state-dependent delay and critical nonlinearity(?)In order to guarantee the uniqueness of solutions,we consider to prove wellposedness in a certain appropriate C~1-type space;secondly,there need an additional term in the energy functional as a compensator for the delay term in the proof of the dissipative property;finally a contractive function is found to obtain the compactness of this concrete equation with critical nonlinearity,thus we establish the existence of a pullback D-attractor.In contrast with the method of quasi-stability estimates,it does not need to assume the damping parameter k is big enough.