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Controlling roughening processes in the stochastic Kuramoto–Sivashinsky equation

Gomes, S.N.; Kalliadasis, S.; 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.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.physd.2017.02.011
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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 Item
Copyright Holders: 2017 The Authors
ISSN: 0167-2789
Project Funding Details:
Funded Project NameProject IDFunding Body
EP/H034587Not SetEPSRC
Keywords: stochastic partial differential equations; stochastic Kuramoto–Sivashinsky equation; roughening processes and surface growth dynamics; fluctuating interfaces; feedback control
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 49243
Depositing User: Marc Pradas
Date Deposited: 24 Apr 2017 14:39
Last Modified: 18 May 2017 03:04
URI: http://oro.open.ac.uk/id/eprint/49243
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