Long time behavior for nonlocal stochastic Kuramoto-Sivashinsky equations

被引：3

作者：

Wang, Guanying ^{[1
]}

Wang, Xingchun ^{[2
,3
]}

Wang, Yongjin ^{[2
,3
,4
]}

机构：

[1] Nankai Univ, Inst Finance & Dev, Tianjin 300071, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[4] Nankai Univ, Sch Business, Tianjin 300071, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2014年 / 87卷

基金：

中国国家自然科学基金;

关键词：

Nonlocal stochastic Kuramoto-Sivashinsky equations; Gaussian processes; Exponentially stable; Second moment stability; PDE CONNECTION; STABILITY; TURBULENCE; DYNAMICS;

D O I：

10.1016/j.spl.2013.12.022

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we consider a class of nonlocal stochastic Kuramoto-Sivashinsky equations driven by additive noises. Under some appropriate conditions, we investigate long time behavior, i.e., stability and growth bounds of the solutions to the equation. Finally, several examples are given to illustrate our results. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：54 / 60

页数：7

共 20 条

[1] A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process [J].

Allouba, H .

COMPTES RENDUS MATHEMATIQUE, 2003, 336 (04) :309-314

[2] Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula [J].

Allouba, H .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (11) :4627-4637

[3]

Allouba H, 2001, ANN PROBAB, V29, P1780

[4] BROWNIAN-TIME BROWNIAN MOTION SIEs ON R+ x Rd: ULTRA REGULAR DIRECT AND LATTICE-LIMITS SOLUTIONS AND FOURTH ORDER SPDEs LINKS [J].

Allouba, Hassan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (02) :413-463

[5]

[Anonymous], 2001, CAM T APP M

[6] On a nonlocal stochastic Kuramoto-Sivashinsky equation with jumps [J].

Bo, Lijun ;

Shi, Kehua ;

Wang, Yongjin .

STOCHASTICS AND DYNAMICS, 2007, 7 (04) :439-457

[7] Large deviation for the nonlocal Kuramoto-Sivashinsky SPDE [J].

Bo, Lijun ;

Jiang, Yiming .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 82 :100-114

[8] STABILITY OF STOCHASTIC PARTIAL-DIFFERENTIAL EQUATION [J].

CURTAIN, RF .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1981, 79 (02) :352-369

[9]

Da Prato G, 1996, ERGODICITY INFINITE

[10] Dynamics of a nonlocal Kuramoto-Sivashinsky equation [J].

Duan, JQ ;

Ervin, VJ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 143 (02) :243-266

← 1 2 →