Optimal design problems for a dynamic viscoelastic plate. I: Short memory material
type: Item
instance of: scholarly article
title: Optimal design problems for a dynamic viscoelastic plate. I: Short memory material
zbMATH Open document ID: 0845.49001
author: Igor Bock
published in: Applications of Mathematics
publication date: 1996-09-04T00:00:00Z
full work available at URL: https://eudml.org/doc/32920
review text: Several optimal control problems with the same state problem -- a pseudohyperbolic variational inequality with a linear operator -- are considered. The control parameters appearing in the coefficients of the variational inequality as well as on the right-hand side are analyzed. The thickness of the dynamic viscoelastic plate with velocity constraints plays the role of control variable. Cost functionals correspond with adjusting the deflection (or the field moments) to a prescribed function \(z_d\) (with minimal cost). Existence of an optimal control is proven on the abstract level. Using the method of penalization an existence and uniqueness theorem for a solution of an initial-boundary value problem for a pseudohyperbolic variational inequality is proved.
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 35L85
Mathematics Subject Classification ID: 74Hxx
zbMATH DE Number: 829871
zbMATH Keywords: variable thickness
zbMATH Keywords: optimal control
zbMATH Keywords: viscoelastic plate
zbMATH Keywords: penalization
zbMATH Keywords: pseudohyperbolic variational inequality
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
cites work: Q4159877
cites work: Optimal Control of a Viscoelastic Plate Bending with Respect to a Thickness
cites work: An optimal control problem for a pseudoparabolic variational inequality
cites work: Q4777920
cites work: Q3338836
cites work: Optimal control of nonsmooth distributed parameter systems
OpenAlex ID: W2613393248
DOI: 10.21136/AM.1995.134295
description: scientific article; zbMATH DE number 829871