An optimal control problem for a pseudoparabolic variational inequality
type: Item
instance of: scholarly article
title: An optimal control problem for a pseudoparabolic variational inequality
zbMATH Open document ID: 0772.49008
published in: Applications of Mathematics
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/15701
review text: The paper deals with an optimal control problem described by: \(u(t,e)\in K(e)\) for a.e. \(t\in [0,T]\), for a.e. \(t\in [0,T]: \langle A(t,e)u'(t,e)+B(t,e)u(t,e)\), \(v-u(t,e)\rangle\geq \langle f(t,e)\), \(v- u(t,e)\rangle\) for all \(v\in K(e)\), \(u(0,e)=u_ 0(e)\in K(e)\), \(j(u(\bar e),\bar e)=\min_{e\in U_{ad}} j(u(e),e)\), where \(A(t,e)\), \(B(t,e)\) are families of elliptic operators operating from the Hilbert space \(V\) into its dual \(V^*\), \(U_{ad}\) is a compact subset of a Banach space \(U\), \(K(e)\) is closed and convex subset of the space \(V\) for every \(e\in U_{ad}\). An existence and uniqueness theorem for a state pseudoparabolic inequality is proved using the penalization method. The existence of an optimal control \(\bar e\) is verified. The theory is applied to the optimal design problem for a viscoelastic plate with an obstacle, where a variable thickness of the plate plays the role of a control parameter.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 74Hxx
zbMATH DE Number: 58781
zbMATH Keywords: optimal control
zbMATH Keywords: elliptic operators
zbMATH Keywords: pseudoparabolic inequality
zbMATH Keywords: optimal design
zbMATH Keywords: viscoelastic plate
author: Igor Bock
author: Jan Lovíšek
reviewed by: Igor Bock
MaRDI profile type: Publication
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OpenAlex ID: W2604120240
DOI: 10.21136/AM.1992.104492
description: scientific article; zbMATH DE number 58781