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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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| Published in: | Journal of dynamical and control systems 2020-10, Vol.26 (4), p.641-661 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c319t-7e7e55d8d5ed4da6820a364ac17e2735d49c475aa6e2a668d7435f6e8c094d263 |
| container_end_page | 661 |
| container_issue | 4 |
| container_start_page | 641 |
| container_title | Journal of dynamical and control systems |
| container_volume | 26 |
| creator | Alekseev, G. V. Brizitskii, R. V. |
| description | 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. |
| doi_str_mv | 10.1007/s10883-019-09474-1 |
| format | article |
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H
s
(Γ)
3
for any
s
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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.</description><subject>Boundary control</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Computational fluid dynamics</subject><subject>Control</subject><subject>Dynamical Systems</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fluid flow</subject><subject>Hydrodynamic equations</subject><subject>Incompressible flow</subject><subject>Incompressible fluids</subject><subject>Magnetic domains</subject><subject>Magnetohydrodynamics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimization</subject><subject>Smoothness</subject><subject>Stability analysis</subject><subject>Systems Theory</subject><subject>Vibration</subject><issn>1079-2724</issn><issn>1573-8698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRSMEEqXwA6wssTbY8TNLKIVWKg8JWFsmdtpUid3aiVD_HrcBsWM1M9K5M6OTZZcYXWOExE3ESEoCES4gKqigEB9lI8wEgZIX8jj1SBQwFzk9zc5iXCOECknkKAt3vndGhx2YeNcF34DX4D8b20ZQ-QC6lQVvne5q7_bMk14629UlmO1M8GbndJuG6bY_EBHU7pC4961O7VfdrcCzd3BurG7A76Xz7KTSTbQXP3WcfTxM3yczuHh5nE9uF7AkuOigsMIyZqRh1lCjucyRJpzqEgubC8IMLUoqmNbc5ppzaQQlrOJWlsmAyTkZZ1fD3k3w297GTq19H1w6qXJKsCSCcZyofKDK4GMMtlKbULfpTYWR2rtVg1uV3KqDW7UPkSEUE-yWNvyt_if1DepcfYA</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>Alekseev, G. V.</creator><creator>Brizitskii, R. V.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201001</creationdate><title>Boundary Control Problems for the Stationary Magnetic Hydrodynamic Equations in the Domain with Non-Ideal Boundary</title><author>Alekseev, G. V. ; Brizitskii, R. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-7e7e55d8d5ed4da6820a364ac17e2735d49c475aa6e2a668d7435f6e8c094d263</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary control</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Computational fluid dynamics</topic><topic>Control</topic><topic>Dynamical Systems</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fluid flow</topic><topic>Hydrodynamic equations</topic><topic>Incompressible flow</topic><topic>Incompressible fluids</topic><topic>Magnetic domains</topic><topic>Magnetohydrodynamics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimization</topic><topic>Smoothness</topic><topic>Stability analysis</topic><topic>Systems Theory</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alekseev, G. V.</creatorcontrib><creatorcontrib>Brizitskii, R. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of dynamical and control systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alekseev, G. V.</au><au>Brizitskii, R. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Boundary Control Problems for the Stationary Magnetic Hydrodynamic Equations in the Domain with Non-Ideal Boundary</atitle><jtitle>Journal of dynamical and control systems</jtitle><stitle>J Dyn Control Syst</stitle><date>2020-10-01</date><risdate>2020</risdate><volume>26</volume><issue>4</issue><spage>641</spage><epage>661</epage><pages>641-661</pages><issn>1079-2724</issn><eissn>1573-8698</eissn><abstract>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
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| 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 |
| title | Boundary Control Problems for the Stationary Magnetic Hydrodynamic Equations in the Domain with Non-Ideal Boundary |
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