학술논문
Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation.
Document Type
Journal
Author
Gomes, S. N. (4-ICL-M) AMS Author Profile; Kalliadasis, S. (4-ICL-KEN) AMS Author Profile; Papageorgiou, D. T. (4-ICL-M) AMS Author Profile; Pavliotis, G. A. (4-ICL-M) AMS Author Profile; Pradas, M. (4-OPEN-MS) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35Q Equations of mathematical physics and other areas of application
35Q53KdV-like equations
35Partial differential equations -- 35R Miscellaneous topics
35R60Partial differential equations with randomness, stochastic partial differential equations
37Dynamical systems and ergodic theory -- 37N Applications
37N35Dynamical systems in control
60Probability theory and stochastic processes -- 60H Stochastic analysis
60H15Stochastic partial differential equations
93Systems theory; control -- 93B Controllability, observability, and system structure
93B52Feedback control
93Systems theory; control -- 93C Control systems
93C20Systems governed by partial differential equations
35Q53
35
35R60
37
37N35
60
60H15
93
93B52
93
93C20
Language
English
Abstract
In this paper the authors study the problem of controlling roughness(the variance) of the surfaces originating from nonlinear stochasticpartial differential equations. Their study is exemplified by thestochastic Kuramoto-Sivashinsky equation with either the Burgersnonlinearity or the Kardar-Parisi-Zhang (KPZ) nonlinearity. They usedistributed or point actuators. The key point is to split the originalequation into a linear stochastic and a nonlinear deterministicequation, which makes it possible to apply linear feedback controlmethods. In the literature, there are many works using nonlinearfeedback controls. Their method offers several distinct advantagessince the controls they use are linear functions of the solution. Theydo not affect the overall dynamics of the system and decrease thecomputational cost. The authors present some computations withoutgiving a theorem.