Optimal control problems for a class of semilinear multisolution elliptic equations
type: Item
instance of: scholarly article
title: Optimal control problems for a class of semilinear multisolution elliptic equations
zbMATH Open document ID: 1040.49028
DOI: 10.1023/A:1025403506651
published in: Journal of Optimization Theory and Applications
publication date: 2004-02-12T00:00:00Z
review text: The paper considers an optimal control problem governed by the elliptic equation \[ \begin{aligned} -\text{div}\bigl(A(x)\nabla & y(x)\bigr)+ f \bigl(x, y(x)\bigr)= u(x)\quad in\;\Omega,\\ & y(x)= 0\quad on\;\partial\Omega,\end{aligned} \] where \(u\) plays the role of the control with a finite set of admissible values. The authors claim the existence of an optimal control and by means of a family of supplementary parabolic optimal control problems derive necessary optimality conditions. The assumptions used in the paper are not clearly stated and the proofs of the existence of optimal controls for the original problem and supplementary problems are not consistent.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2041233
zbMATH Keywords: elliptic equations
zbMATH Keywords: parabolic equations
zbMATH Keywords: optimal control
zbMATH Keywords: closed range
zbMATH Keywords: densely defined operators
zbMATH Keywords: necessary optimality conditions
author: Hang Gao
author: N. H. Pavel
reviewed by: Uldis Raitums
MaRDI profile type: Publication
cites work: Q4172378
cites work: Q4028859
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cites work: Optimal control governed by a semilinear elliptic differential equation
cites work: Optimization and nonsmooth analysis
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full work available at URL: a:1025403506651
OpenAlex ID: W117663424
description: scientific article; zbMATH DE number 2041233