Controllability of One-Dimensional Viscous Free Boundary Flows
Abstract
In this work, we address the local controllability of a one-dimensional free boundary problem for a fluid governed by the viscous Burgers equation. The free boundary manifests itself as one moving end of the interval, and its evolution is given by the value of the fluid velocity at this endpoint. We prove that, by means of a control actuating along the fixed boundary, we may steer the fluid to constant velocity in addition to prescribing the free boundary's position, provided the initial velocities and interface positions are close enough.
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Information & Authors
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Published In
SIAM Journal on Control and Optimization
Pages: 1830 - 1850
DOI: 10.1137/19M1285354
ISSN (online): 1095-7138
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 4 September 2019
Accepted: 19 February 2021
Published online: 6 May 2021
Keywords
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Authors
Funding Information
Alexander von Humboldt-Stiftung https://doi.org/10.13039/100005156
Funding Information
Air Force Office of Scientific Research https://doi.org/10.13039/100000181 : FA9550-18-1-0242
Funding Information
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659
Funding Information
Horizon 2020 Framework Programme https://doi.org/10.13039/100010661 : 765579-ConFlex
Funding Information
Horizon 2020 Framework Programme https://doi.org/10.13039/100010661 : 694126-DyCon
Funding Information
Ministerio de Economía, Industria y Competitividad, Gobierno de España https://doi.org/10.13039/501100010198 : MTM2017-92996-C2-1-R
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