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具强阻尼的随机sine-Gordon方程的随机吸引子存在性 被引量：6

Existence of Random Attractor for Strongly Damped Stochastic sine-Gordon Equation
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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. 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
作者 尹福其 周盛凡 李红艳
机构地区 上海大学理学院
出处 《上海大学学报（自然科学版）》 CAS CSCD 北大核心 2006年第3期260-265,共6页 Journal of Shanghai University:Natural Science Edition
基金 国家自然科学基金资助项目(10471086)
关键词 强阻尼 随机微分方程 随机吸引子 WIENER过程 strongly damped stochastic differential equation random attractor Wiener process
分类号 O193 [理学—基础数学] O211.63 [理学—概率论与数理统计]
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参考文献11

  • 1ZHOU S.Global attractor for strongly damped nonlinear wave equations[J].Function Differential Equation,1999,6(3-4):451-470.
  • 2ZHOU S.Dimention of the global attractor for strongly damped nonlinear wave equations[J].J Math Anal Appl,1999,233:102-115.
  • 3CRAUEL H,FLANDOLI F.Attractors for random dynamical systems[J].Probability Theory and Related Fields,1994,100(3):365-393.
  • 4DEBUSSCHE A.On the finite dimensionality of randomattractors[J].Stochastic Analysis and Applications,1997,15(4):473-491.
  • 5TEMAM R.Infinite-dimensional dynamical systems in mechanics and physics[M].2nd ed.New York:Appl Math Sci,Springer-Verlag,1997,68:21-22.
  • 6CARABALLO T,LANGA J A,VALERO J.Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise[J].J Math Anal Appl,2001,260(2):602-622.
  • 7FAN X.Random attractor for a damped sine-Gordon equation with white noise[J].Pacific J Math,2004,216 (1):63-76.
  • 8CRAUEL H,DEBUSSCHE A,FLANDOLI F.Random attractors[J].J of Dynamics and Differential Equations,1997,9(2):307-341.
  • 9MASSATT P.Limiting behaviour for a strong damped nonlinear wave equation[J].J Diff Equ,1983,48:334-349.
  • 10PRATO G D,ZABCZYK J.Stochastic equations in infinite dimensions[M].London:Cambridge University Press,1992:115-236.

同被引文献30

  • 1蒲云.Hilbert空间上非凸规划的Kuhn-Tucker鞍点定理[J].重庆建筑工程学院学报,1989,11(3):98-105. 被引量：1
  • 2姚喜妍.2×2算子矩阵的逆[J].数学学报（中文版）,2006,49(4):949-954. 被引量：2
  • 3ZHOU S F.Global attractor for strongly damped nonlinear wave equations[J].Functional Differential Equations,1999,6(3-4):451-470.
  • 4FAN X M.Random attractor for a damped Sine-Gordon equation with white noise[J].Pacific J Math,2007,19(1):63-76.
  • 5CRAUEL H,DEBUSSCHE A,FLANDOLI F.Random attractors[J].J of Dynamics and Differential Equations,1997,9(2):307-341.
  • 6CRAUEL H,FLANDOLI F.Attractors for random dynamical systems[J].Probability Theory and Related Fields,1994,100(3):365-393.
  • 7Debussche A.On the finite dimensionality of random attractors[J].Stochastic Analysis and Application,1997,15(4):473-491.
  • 8TEMAM R.Infinite Dimensional Dynamical Systems in Mechanics and Physics[M].New York:Springer-Verlag,1998.
  • 9MASSATT P.Limiting behaviour for a strong damped nonlinear wave equation[J].J Diff Equ,1983,48:334-349.
  • 10PRATO G D,ZABCZYK J.Stochastic equations in infinite dimensions[M].London:Cambridge University Press,1992:115-236.

引证文献6

二级引证文献7

上海大学学报（自然科学版）
2006年 第3期

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