Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
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DOI：
10.1016/j.physd.2017.02.011
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发表时间：
2017-06-01
影响因子：
4
通讯作者：
Pradas, M.
中科院分区：
文献类型：
--
作者：
Gomes, S. N.;Kalliadasis, S.;Pradas, M.
以随机的Kuramoto-Sivashinsky方程为例，提出了一种新的控制方法来控制一维半线性抛物型随机偏微分方程解的粗化过程。将原方程分解为线性随机方程和非线性确定性方程，从而可以应用线性反馈控制方法。然后，我们的控制策略基于两个步骤：第一，稳定确定性部分的零解，第二，控制随机线性方程的粗糙度。我们同时考虑周期控制和点驱动控制，在所有情况下都观察到解的二阶矩按照幂定律时间演化，直到它在期望的控制值饱和。(C)2017年作者。爱思唯尔出版公司(Elsevier B.V.)
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. (C) 2017 The Authors. Published by Elsevier B.V.