On the ``bang-bang'' principle for nonlinear evolution inclusions
type: Item
instance of: scholarly article
title: On the ``bang-bang'' principle for nonlinear evolution inclusions
zbMATH Open document ID: 0927.34010
author: A. A. Tolstonogov
author: D. A. Tolstonogov
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1999-07-20T00:00:00Z
review text: The authors deal with the existence of solutions to an evolution inclusion of the form \[ x'(t) +A(t,x(t))\in{F(t,x(t))}\quad\text{a.e., }x(0)=x_{0}, \] in a Banach space, where the right-hand side is not necessarily convex-valued. It is an improvement of results by \textit{N. S. Papageorgiou} [Dyn. Syst. Appl. 2, No. 1, 61-74 (1993; Zbl 0780.34045)]. Actually, the paper is divided into four sections. After presenting the introduction and some necessary preliminaries the authors investigate the existence of extreme solutions. Next, they show that these solutions form a dense subset in the solution set with convexified right-hand side. In the fifth section the authors derive a version of the bang-bang principle for control systems and finally, the paper closes with an example of a nonlinear parabolic control problem.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1286183
zbMATH Keywords: equations with multivalued right-hand sides
zbMATH Keywords: extreme solutions
zbMATH Keywords: bang-bang principle
reviewed by: George Karakostas
MaRDI profile type: Publication
full work available at URL: s000300050067
OpenAlex ID: W1986110230
DOI: 10.1007/S000300050067
description: scientific article; zbMATH DE number 1286183