Nonconvex evolution inclusions generated by time-dependent subdifferential operators

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 th...

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Bibliographic Details
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
Description
Summary: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.

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