Minimizing movements for dissipative systems that are not gradient flows

The time discretization method, which is a method of constructing time global solutions for gradient flows, is applied to dissipative systems in Hilbert spaces, which are not necessarily gradient flows. Equations with perturbation terms added to gradient flows are considered, and when the perturbation term is smaller than the principal term in an analytical sense, the dissipative structure of the energy is maintained, and the existence of time global solutions is shown by the time discretization method.