Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
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Published version
Author(s)
Noronha Moreira Antunes Gomes, ST
Kalliadasis, S
Papageorgiou, DT
Pavliotis, GA
Pradas, M
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.
Date Issued
2017-03-01
Date Acceptance
2017-02-22
Citation
Physica D - Nonlinear Phenomena, 2017, 348, pp.33-43
ISSN
0167-2789
Publisher
Elsevier
Start Page
33
End Page
43
Journal / Book Title
Physica D - Nonlinear Phenomena
Volume
348
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/).
This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
License URL
Sponsor
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)
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
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Multidisciplinary
Physics, Mathematical
Mathematics
Physics
Stochastic partial differential equations
Stochastic Kuramoto-Sivashinsky equation
Roughening processes and surface growth dynamics
Fluctuating interfaces
Feedback control
THIN-FILM DEPOSITION
PARTIAL-DIFFERENTIAL-EQUATIONS
SURFACE-ROUGHNESS
PREDICTIVE CONTROL
SPUTTERING PROCESS
FEEDBACK-CONTROL
SCALE PROPERTIES
GROWTH
POROSITY
MODEL
0102 Applied Mathematics
Fluids & Plasmas
Publication Status
Published