On the variational stability of a class of nonlinear parabolic optimal control problems
type: Item
instance of: scholarly article
title: On the variational stability of a class of nonlinear parabolic optimal control problems
zbMATH Open document ID: 0844.49020
DOI: 10.4171/ZAA/697
author: Nikolaos S. Papageorgiou
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-09-03T00:00:00Z
review text: Summary: In this paper we study parametric optimal control problems governed by a nonlinear parabolic equation in divergence form. The parameter appears in all the data of the problem, including the partial differential operator. Using as tools the \(G\)-convergence of operators and the \(\Gamma\)-convergence of functionals, we show that the set-valued map of optimal pairs is upper-semicontinuous with respect to the parameter and the optimal value function responds continuously to changes of the parameter. Finally, in the case of semilinear systems, we show that our framework can also incorporate systems with weakly convergent coefficients.
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 856815
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: evolution triples
zbMATH Keywords: monotone operators
zbMATH Keywords: compact embeddings
zbMATH Keywords: upper-semicontinuous multifunctions
zbMATH Keywords: parametric optimal control
zbMATH Keywords: nonlinear parabolic equation
zbMATH Keywords: \(G\)-convergence
zbMATH Keywords: \(\Gamma\)-convergence
zbMATH Keywords: semilinear systems
MaRDI profile type: Publication
cites work: Gamma-convergence and optimal control problems
cites work: An introduction to \(\Gamma\)-convergence
cites work: On continuous approximations for multifunctions
cites work: Q4730340
cites work: G-convergence of a class of evolution operators
cites work: Q5601627
cites work: On the set of solutions of a class of nonlinear evolution inclusions
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Optimal control in coefficients for weak variational problems in Hilbert space
cites work: Q5562938
Recommended article: On the variational stability of a class of nonlinear parabolic optimal control problems
Recommended article: Q3695907
Recommended article: Stability for semilinear parabolic optimal control problems with respect to initial data
Recommended article: Q3210448
Recommended article: The variational stability of an optimal control problem for Volterra-type equations
Recommended article: On a class of optimal control problems for parabolic equations
Recommended article: On Existence, Uniqueness, and Convergence of Optimal Control Problems Governed by Parabolic Variational Inequalities
Recommended article: Optimal control of parabolic variational inequalities
Recommended article: Controllability for nonlinear variational inequalities of parabolic type
Recommended article: Controllability for variational inequalities of parabolic type with nonlinear perturbation
description: scientific article; zbMATH DE number 856815