Nonconvex evolution inclusions generated by time-dependent subdifferential operators (Q1818335)

Summary: We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials \(\partial\phi(t,x)\) without assuming that \(\phi(t,\cdot)\) is of compact type. We show the existence of extremal solutions, and then we prove a strong relaxation theorem. Moreover, we show that under a Lipschitz condition on the orientor field, the solution set of the nonconvex problem is path-connected in \(C(T,H)\). These results are applied to nonlinear feedback control systems to derive nonlinear infinite dimensional versions of the ``bang-bang principle''. The abstract results are illustrated by two examples of nonlinear parabolic problems and an example of a differential variational inequality.