The Kurdyka-{L}ojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems

We state and prove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite dimensional Hilbert spaces. One feature is that in this general setting the assumption on the range of the solution can be considerably relaxed, which considerably simplifies the applicability of the stabilisation result even in the case of smooth energies.