Nonconvex evolution inclusions generated by time-dependent subdifferential operators

• Published in: Journal of Applied Mathematics and Stochastic Analysis
• Main Authors: Arseni-Benou, K, Halidias, N, Papageorgiou, NS
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: 1999
• Subjects: Feedback Control System; Parabolic Equation; Path-Connected; Strong Relaxation; Strong Solution; Subdifferential; North Atlantic
• Online Access: http://dspace.lib.ntua.gr/handle/123456789/13262; https://doi.org/10.1155/S1048953399000222

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,r 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. ©1999 by North Atlantic Science Publishing Company.