Convergence and optimal control problems of nonlinear evolution equations governed by time-dependent operator

We study an abstract nonlinear evolution equation governed by a time-dependent operator of subdifferential type in a real Hilbert space. In this paper we discuss the convergence of solutions to our evolution equations. Also, we investigate the optimal control problems of nonlinear evolution equations. Moreover, we apply our abstract results to a quasilinear parabolic PDE with a mixed boundary condition.