Existence of solutions for a class of nonlinear control problems
type: Item
instance of: scholarly article
title: Existence of solutions for a class of nonlinear control problems
zbMATH Open document ID: 0681.49009
DOI: 10.1007/BF00940530
author: Yanyan Li
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: We consider problems of control and problems of optimal control, monitored by an abstract equation of the form \(Ex=N_ ux\) in a finite interval [0,T]; here, x is the state variable with values in a reflexive Banach space; u is the control variable with values in a metric space; E is linear and monotone; and \(N_ u\) is nonlinear of the Nemitsky type. Thus, by well-known devices, the results apply also to parabolic partial differential equations in a cylinder [0,T]\(\times G\), \(G\subset {\mathbb{R}}^ n\), with Cauchy data for \(t=0\) and Dirichlet or Neumann conditions on the lateral surface of the cylinder. We prove existence theorems for solutions and existence theorems for optimal solutions, by reduction to a theorem of \textit{N. Kenmochi} [Hiroshima Math. J. 1, 435-443 (1971; Zbl 0262.47043)] for reflexive Banach spaces.
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 4115371
zbMATH Keywords: maximal monotone operators
zbMATH Keywords: measurable selections
zbMATH Keywords: optimal control
zbMATH Keywords: Nemitsky type
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00940530
OpenAlex ID: W2086476602
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description: scientific article; zbMATH DE number 4115371