Nonconvex evolution inclusions generated by time-dependent subdifferential operators. (1999) - Arseni-Benou, Kate; Halidias, Nikolaos; Papageorgiou, Nikolaos S.
Abstract : We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials ∂ ϕ ( t, x ) without assuming that ϕ ( t, . ) 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.