Generalized φ-Pullback Attractors in Time-Dependent Spaces: Application to a Nonautonomous Wave Equation With Time-Dependent Propagation Velocity

We present sufficient conditions to obtain a generalized-pullback attractor for evolution processes on time-dependent phase spaces, where is a given decay function and is a given universe. We deal specifically with the case in which has either exponential or polynomial decay, the universe is the one of uniformly bounded families, and apply the abstract results to a non-autonomous wave equation with time-dependent propagation velocity.