摘要
研究非自治随机sine-Gordon方程所生成的随机动力系统φ的D-周期吸引子的存在唯一性.运用一致估计得到了D的D-吸收集的存在性,并用分解技巧,证明了φ的渐近紧性,建立了动力系统φ在H^1(R^n)×L^2(R^n)中的D-周期吸引子的存在唯一性.当非自治外力项具有周期性时,该D-吸引子也呈现相同的周期性.
We concerns on the existence and uniqueness of periodic-attractor for random dynamical system φ generated by sine-Gordon equation with non-autonomous term as well as stochastic term.Firstly,a D-pullback absorbing set of φ is obtained by uniform estimates.Secondly,by applying a splitting technique,the asymptotic compactness of φ is proved.Finally,the existence and uniqueness of periodic D-attractor of the corresponding random dynamical system in H^1(R^n) × L^2{R^n) is established.Moreover,the D-pullback attractor is proved to be periodic when the random dynamical system contains a periodic deterministic forcing term.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2014年第6期1127-1140,共14页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金11171280
11101054
省教育厅基金12C0408
湘潭大学博士后资助项目湖南省高校创新平台开放基金(11K010)
