On the Unique Solvability of the Optimal Starting Control Problem for the Linearized Equations of Motion of a Viscoelastic Medium

We study an optimization problem for the linearized evolution equations of the Oldroyd model of motion of a viscoelastic medium. The equations are given in a bounded three-dimensional domain. The velocity distribution at the initial time is used as a control function. The objective functional is ter...

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Bibliographic Details
Published inDifferential equations Vol. 57; no. 8; pp. 1070 - 1075
Main Author Artemov, M. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2021
Springer
Springer Nature B.V
Subjects
Analysis
Control Theory
Difference and Functional Equations
Differential equations
Equations of motion
Fluid dynamics
Linearization
Mathematics
Mathematics and Statistics
Optimal control
Optimization
Ordinary Differential Equations
Partial Differential Equations
Velocity distribution
Viscoelasticity
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Summary:We study an optimization problem for the linearized evolution equations of the Oldroyd model of motion of a viscoelastic medium. The equations are given in a bounded three-dimensional domain. The velocity distribution at the initial time is used as a control function. The objective functional is terminal. The existence of a unique optimal control is proved for a given set of admissible controls. A variational inequality characterizing the optimal control is derived.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266121080115