Abstract: In this paper,we proved that the infinitesimal generator of a strongly continuous co- sine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space X(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed. 

Key words:  , dual cosine operator function, time-dependent perturbation, θ-reflexivity