Existence of solution in thickness optimization problem for a plate
type: Item
instance of: scholarly article
title: Existence of solution in thickness optimization problem for a plate
zbMATH Open document ID: 0881.73098
DOI: 10.1007/BF02366538
author: V. N. Brusnikin
published in: Cybernetics and Systems Analysis
publication date: 1998-02-19T00:00:00Z
review text: We consider the optimization of one of the linear parameters of a thin plate subject to dynamic forces. The problem is formulated as an optimal control problem for partial differential equations with phase constraints, and the existence of solution is proved by using the Weierstrass theorem. However, the application of this theorem requires a proof of compactness of the feasible set. Here compactness of the feasible set is proved using continuous dependence of the solution of partial differential equations of fourth order on input values (the coefficients, the right-hand side, and the initial conditions).
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 1051118
zbMATH Keywords: compactness of feasible set
zbMATH Keywords: continuous dependence of solution on input values
zbMATH Keywords: optimal control problem
zbMATH Keywords: phase constraints
zbMATH Keywords: Weierstrass theorem
MaRDI profile type: Publication
cites work: Q3783431
cites work: Solvability in the small of nonstationary problems for incompressible ideal and viscous fluids and the case of vanishing viscosity
cites work: Q5576518
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description: scientific article; zbMATH DE number 1051118