Boundary Control Problems for the Stationary Magnetic Hydrodynamic Equations in the Domain with Non-Ideal Boundary

Boundary control problems for a stationary model of magnetohydrodynamics of a viscous incompressible fluid are considered in a domain with non-ideal boundary. The role of the control is played by a tangential component of a magnetic field specified on an entire boundary. In the case when the control...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2020-10, Vol.26 (4), p.641-661
Main Authors: Alekseev, G. V., Brizitskii, R. V.
Format: Article
Language:English
Subjects:
Boundary control
Calculus of Variations and Optimal Control
Optimization
Computational fluid dynamics
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Fluid flow
Hydrodynamic equations
Incompressible flow
Incompressible fluids
Magnetic domains
Magnetohydrodynamics
Mathematics
Mathematics and Statistics
Optimization
Smoothness
Stability analysis
Systems Theory
Vibration
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Summary:Boundary control problems for a stationary model of magnetohydrodynamics of a viscous incompressible fluid are considered in a domain with non-ideal boundary. The role of the control is played by a tangential component of a magnetic field specified on an entire boundary. In the case when the control function is square integrable, the solvability of the control problem is proved. Under assumption that control possesses a higher smoothness described by the space H s (Γ) 3 for any s > 0, an optimality system is derived. Based on the analysis of an optimality system, the local stability estimates of optimal solutions are established with respect to small perturbations of a cost functional.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-019-09474-1