On nonlinear, nonconvex evolution inclusions

Abstract

We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, Gδ-subset of the solution set of the original Cauchy problem. As an application, we obtain "bang-bang" type theorems for two nonlinear parabolic distributed parameter control systems. © 1995, Tokyo Institute of Technology. All Rights Reserved.

Document Type

Article

DOI

https://doi.org/10.2996/kmj/1138043481

Keywords

Extremal solution, Integral solution, M-accretive operator, Nonlinear semigroup, Parabolic system, Strong relaxation theorem

Publication Date

1-1-1995

Journal Title

Kodai Mathematical Journal

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