On a nonlocal stochastic Kuramoto-Sivashinsky equation with jumps

被引：16

作者：

Bo, Lijun ^{[1
,2
]}

Shi, Kehua ^{[2
]}

Wang, Yongjin ^{[2
]}

机构：

[1] Xidian Univ, Dept Math, Xian 710071, Peoples R China

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

来源：

STOCHASTICS AND DYNAMICS | 2007年 / 7卷 / 04期

基金：

美国国家科学基金会;

关键词：

nonlocal Kuramoto-Sivashinsky equation; Poisson random measure; invariant measure;

D O I：

10.1142/S0219493707002104

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 study a class of nonlocal stochastic Kuramoto-Sivashinsky equations driven by compensated Poisson random measures and show the existence and uniqueness of the weak solution to the equation. Furthermore, we prove that an invariant measure of the equation indeed exists under some appropriate assumptions.

引用

页码：439 / 457

页数：19

共 12 条

[1] Ergodicity for nonlinear stochastic equations in variational formulation [J].

Barbu, V ;

Prato, G .

APPLIED MATHEMATICS AND OPTIMIZATION, 2006, 53 (02) :121-139

[2]

Da Prato G, 1996, ERGODICITY INFINITE

[3] One-dimensional stochastic Burgers equation driven by Levy processes [J].

Dong, Z. ;

Xu, T. G. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 243 (02) :631-678

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

Duan, JQ ;

Ervin, VJ .

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

[5] On the stochastic Kuramoto-Sivashinsky equation [J].

Duan, JQ ;

Ervin, VJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 44 (02) :205-216

[6]

Ikeda N., 1989, STOCHASTIC DIFFERENT, DOI DOI 10.1002/BIMJ.4710320720

[7]

JAMES A, 2001, J INEQUALITIES PURE, V2, P1

[8]

Kim JU, 2006, J DIFFER EQUATIONS, V228, P737, DOI 10.1016/j.jde.2005.11.005

[9]

Pardoux E., 1979, Stochastics, V3, P127, DOI 10.1080/17442507908833142

[10]

Robinson J. C., 2001, CAM T APP M

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