Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation

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Title: Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
Author(s): Noronha Moreira Antunes Gomes, ST
Kalliadasis, S
Papageorgiou, DT
Pavliotis, GA
Pradas, M
Item Type: Journal Article
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.
Publication Date: 1-Mar-2017
Date of Acceptance: 22-Feb-2017
URI: http://hdl.handle.net/10044/1/44914
DOI: https://dx.doi.org/10.1016/j.physd.2017.02.011
ISSN: 0167-2789
Publisher: Elsevier
Journal / Book Title: Physica D - Nonlinear Phenomena
Copyright Statement: © 2017 The Authors.Published by Elsevier B.V. This is an open access article under the CC-BY license (http://creativecommons.org/licenses/by/4.0/).
Sponsor/Funder: Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: 247031
EP/J009636/1
EP/H034587/1
EP/K041134/1
EP/K008595/1
EP/L025159/1
EP/L020564/1
EP/L024926/1
EP/L027186/1
Keywords: Fluids & Plasmas
0102 Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Chemical Engineering
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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