Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise

被引：0

作者：

Gao, Peng ^{[1
,2
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Changchun 130024, Peoples R China

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2022年 / 28卷

关键词：

Irreducibility; Kuramoto-Sivashinsky equation; degenerate noise; approximate controllability; Agrachev-Sarychev method; NAVIER-STOKES EQUATIONS; NULL-CONTROLLABILITY; TRAJECTORIES; DYNAMICS;

D O I：

10.1051/cocv/2022014

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number of Fourier modes. In order to obtain the irreducibility, we first investigate the approximate controllability of Kuramoto-Sivashinsky equation driven by a finite-dimensional force, the proof is based on Agrachev-Sarychev type geometric control approach. Next, we study the continuity of solving operator for deterministic Kuramoto-Sivashinsky equation. Finally, combining the approximate controllability with continuity of solving operator, we establish the irreducibility of Kuramoto-Sivashinsky equation.

引用

页数：22

共 46 条

[1] Adams R. A., 2003, Sobolev Spaces
[2] Navier-Stokes equations: Controllability by means of low modes forcing
Agrachev, AA
Sarychev, AV
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2005, 7 (01) : 108 - 152
[3] Agrachev A, 2008, INT MAT SER, V6, P1
[4] Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing
Agrachev, Andrey A.
Sarychev, Andrey V.
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 265 (03) : 673 - 697
[5] Feedback control of the Kuramoto-Sivashinsky equation
Armaou, A
Christofides, PD
[J]. PHYSICA D, 2000, 137 (1-2): : 49 - 61
[6] Barbu V, 2005, NONCON OPTIM ITS APP, V79, P147
[7] Irreducibility of the transition semigroup associated with the stochastic obstacle problem
Barbu, V
Da Prato, G
[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2005, 8 (03) : 397 - 406
[8] Barbu V., 2005, STOCHASTIC PARTIAL D, V7, P21
[9] On a nonlocal stochastic Kuramoto-Sivashinsky equation with jumps
Bo, Lijun
Shi, Kehua
Wang, Yongjin
[J]. STOCHASTICS AND DYNAMICS, 2007, 7 (04) : 439 - 457
[10] Large deviation for the nonlocal Kuramoto-Sivashinsky SPDE
Bo, Lijun
Jiang, Yiming
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 82 : 100 - 114

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