The Library
Stabilizing non-trivial solutions of the generalized Kuramoto-Sivashinsky equation using feedback and optimal control
Tools
Gomes, Susana N., Papageorgiou, Demetrios and Pavliotis, G. A. (2016) Stabilizing non-trivial solutions of the generalized Kuramoto-Sivashinsky equation using feedback and optimal control. IMA Journal of Applied Mathematics, 82 (1). pp. 158-194. doi:10.1093/imamat/hxw011 ISSN 0272-4960.
|
PDF
WRAP-stabilizing-non-trivial-solutions-generalized-Kuramoto-Sivashinsky-equation-feedback-optimal-control-Gomes-2016.pdf - Accepted Version - Requires a PDF viewer. Download (3174Kb) | Preview |
Official URL: https://doi.org/10.1093/imamat/hxw011
Abstract
The problem of controlling and stabilizing solutions to the Kuramoto–Sivashinsky (KS) equation is studied in this paper. We consider a generalized form of the equation in which the effects of an electric field and dispersion are included. Both the feedback and optimal control problems are studied. We prove that we can control arbitrary non-trivial steady states of the KS equation, including travelling wave solutions, using a finite number of point actuators. The number of point actuators needed is related to the number of unstable modes of the equation. Furthermore, the proposed control methodology is shown to be robust with respect to changing the parameters in the equation, e.g. the viscosity coefficient or the intensity of the electric field. We also study the problem of controlling solutions of coupled systems of KS equations. Possible applications to controlling thin film flows are discussed. Our rigorous results are supported by extensive numerical simulations.
Item Type: | Journal Article | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Mathematical models, Liquid films -- Mathematical models, Fluid dynamics -- Mathematical models | ||||||||||||||||||||||||
Journal or Publication Title: | IMA Journal of Applied Mathematics | ||||||||||||||||||||||||
Publisher: | Oxford University Press | ||||||||||||||||||||||||
ISSN: | 0272-4960 | ||||||||||||||||||||||||
Official Date: | 17 March 2016 | ||||||||||||||||||||||||
Dates: |
|
||||||||||||||||||||||||
Volume: | 82 | ||||||||||||||||||||||||
Number: | 1 | ||||||||||||||||||||||||
Page Range: | pp. 158-194 | ||||||||||||||||||||||||
DOI: | 10.1093/imamat/hxw011 | ||||||||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Susana N. Gomes, Demetrios T. Papageorgiou, Grigorios A. Pavliotis, Stabilizing non-trivial solutions of the generalized Kuramoto–Sivashinsky equation using feedback and optimal control: Lighthill–Thwaites Prize, IMA Journal of Applied Mathematics, Volume 82, Issue 1, February 2017, Pages 158–194, https://doi.org/10.1093/imamat/hxw011 is available online at: https://doi.org/10.1093/imamat/hxw011 | ||||||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||||||||
Date of first compliant deposit: | 28 October 2019 | ||||||||||||||||||||||||
Date of first compliant Open Access: | 30 October 2019 | ||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
|
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year