具强阻尼的随机sine-Gordon方程的随机吸引子存在性

上海大学学报(自然科学版)

具强阻尼的随机sine-Gordon方程的随机吸引子存在性

尹福其,周盛凡,李红艳

上海大学理学院，上海 200444

收稿日期:2005-07-15 修回日期:1900-01-01 出版日期:2006-06-30 发布日期:2006-06-30
通讯作者: 周盛凡

Existence of Random Attractor for Strongly Damped-Stochastic sine-Gordon Equation

YIN Fu-qi,ZHOU Sheng-fan,LI Hong-yan

School of Sciences, Shanghai University, Shanghai 200444, China

Received:2005-07-15 Revised:1900-01-01 Online:2006-06-30 Published:2006-06-30
Contact: ZHOU Sheng-fan

摘要/Abstract

摘要： 该文考虑了一个具强阻尼的随机 sine-Gordon方程. 通过引入加权范数与对关于时间为一阶的发展方程对应的线性算子正性的分解, 证明了由该方程生成的随机动力系统的随机紧吸引子的存在性.

关键词: Wiener 过程, 强阻尼, 随机微分方程, 随机吸引子

Abstract:

A strongly damped stochastic sineGordon equation is considered. By introducing weight norm and splitting positivity of the linear operator in the corresponding evolution equation of the first order with respect to time, existence of a compact random attractor is shown for a stochastic dynamical system generated by strongly damped sineGordon equations with white noise.

Key words: random attractor, stochastic differential equation, Wiener process

strongly damped

尹福其;周盛凡;李红艳. 具强阻尼的随机sine-Gordon方程的随机吸引子存在性[J]. 上海大学学报(自然科学版).

YIN Fu-qi;ZHOU Sheng-fan;LI Hong-yan.

Existence of Random Attractor for Strongly Damped-Stochastic sine-Gordon Equation

[J]. Journal of Shanghai University（Natural Science Edition）.