An extension of the concept of gradient semigroups which is stable under perturbation (Q1014716)

The authors introduce the class of gradient-like nonlinear semigroups in a Banach space which is situated strictly between the classes of gradient nonlinear semigroups and nonlinear semigroups with a gradient-like attractor. It is shown that gradient-like nonlinear semigroups are stable under perturbations. Moreover, this result is generalized to the non-autonomous case (for gradient-like evolution processes). The authors also give a characterization of global attractors for gradient-like nonlinear semigroups and evolution processes.