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Controlling roughening processes in the stochastic Kuramoto–Sivashinsky equation
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Gomes, Susana N., Kalliadasis, Serafim, Papageorgiou, D. T., Pavliotis, G. A. and Pradas, M. (2017) Controlling roughening processes in the stochastic Kuramoto–Sivashinsky equation. Physica D: Nonlinear Phenomena, 348 . pp. 33-43. doi:10.1016/j.physd.2017.02.011 ISSN 0167-2789.
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Official URL: https://doi.org/10.1016/j.physd.2017.02.011
Abstract
We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value.
Item Type: | Journal Article | |||||||||||||||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations, Stochastic partial differential equations -- Numerical solutions, Differential equations, Nonlinear | |||||||||||||||||||||||||||||||||
Journal or Publication Title: | Physica D: Nonlinear Phenomena | |||||||||||||||||||||||||||||||||
Publisher: | Elsevier BV | |||||||||||||||||||||||||||||||||
ISSN: | 0167-2789 | |||||||||||||||||||||||||||||||||
Official Date: | 1 June 2017 | |||||||||||||||||||||||||||||||||
Dates: |
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Volume: | 348 | |||||||||||||||||||||||||||||||||
Page Range: | pp. 33-43 | |||||||||||||||||||||||||||||||||
DOI: | 10.1016/j.physd.2017.02.011 | |||||||||||||||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||||||||||||||
Date of first compliant deposit: | 28 October 2019 | |||||||||||||||||||||||||||||||||
Date of first compliant Open Access: | 31 October 2019 | |||||||||||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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