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动力系统中紧的指数吸引集的存在性

THE EXISTENCE OF COMPACT EXPONENTIAL ATTRACTING SET FOR DYNAMICAL SYSTEMS
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摘要 本文研究了一般形式的无穷维动力系统.利用非紧性测度理论,当非紧性测度指数衰减时,获得了紧的指数吸引集的存在性条件.同时给出了易于验证非紧性测度指数衰减的方法. In this article,a general dynamical system is considered.By using the measure of non-compactness theory,the existence of compact exponential attracting set is obtained when the measure of non-compactness exponentially decays.Also a method is given for proving the measure of non-compactness decays exponentially.
作者 李永军 臧子龙
机构地区 兰州城市学院数学学院
出处 《数学杂志》 CSCD 北大核心 2010年第5期891-896,共6页 Journal of Mathematics
基金 国家自然科学基金资助项目(10771159) 甘肃省教育厅科研资助项目(0711B-05)
关键词 动力系统 非紧性测度 吸引子 吸收集 dynamical system measure of non-compactness attractor absorbing set
分类号 O175.21 [理学—基础数学]
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参考文献12

  • 1Cheban D N.Global attractors of Non-autonomous dissipative dynamical systems[M].Sinapore:World Scientific Publishing Co.Pte.Ltd.,2004.
  • 2Chepyzhov V,Vishik M.Attractors for equations of mathematics physics[M].Providence,RI:AMS,2002.
  • 3Teman R.Infinite-dimensional dynamical systems in mechanics and physics[M].New York:Springer,1997.
  • 4李永军,张艳红.R^N上部分耗散反应扩散方程全局吸引子的存在性[J].陕西师范大学学报（自然科学版）,2009,37(3):13-16. 被引量：1
  • 5Ma Q,Wang S,Zhong C.Necessary and sufficient condition for the existence of global attractors for semigroups and applications[J].Mathematics Journal of Indiana University,2002,51:1541-1559.
  • 6Zhong C,Yang M H,Sun C Y.The existenc of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations[J].J.Differential Equations,2006,223:367-399.
  • 7Miranville A.Exponential attractors for a class of evolution equations by a decomposition method[J].Comptes Rendus de l'Acad é mie des Sciences,Series I,Mathematics,1999,328:145-150.
  • 8Málek J,Pra(z)a(k) D.Large time behavior via the method of l-trajectories[J].J.Differential Equations,2002,181:243-279.
  • 9Pra(z)a(k) D.On finite fractal dimension of the global attractor for the wave equation with nonlinear damping[J].Journal of Dynamical and Difference Equation,2002,14:763-776.
  • 10Pra(z)a(k) D.A necessary and sufficient condition for the existence of an exponential attractor[J].Central European J.Mathematics,2003,3:411-417.

二级参考文献9

  • 1Marion M. Finite-dimension attractors associated to partly dissipative reaction-diffusion systems[J]. SIAM Journal of Mathematical Analysis, 1989, 20: 816-844.
  • 2Marion M. Inertial manifolds associated to partly dissipative reaction-diffusion systems [J ]. Journal of Mathematical Analysis and Application, 1989, 143: 295-326.
  • 3Shao Z. Existence of inertial manifolds for partly dissipative reaction-diffusion systems in higher spaee dimensions [ J ]. Journal of Differential Equations, 1998, 144:1-43.
  • 4Teman R. Infinite-dimensional dynamical systems in mechanics and physics [ M]. New York: Springer, 1997.
  • 5Chepyzhov V, Vishik M. Attractors for equations of mathematics physics [ M ]. Providence: American Mathematical Society Colloquium Publications, 2002: 27-50.
  • 6Wang B. Attractors for reaction diffusion equation in unbounded domains[J]. Physics D, 1999, 128: 41-52.
  • 7Yang M, Sun C, Zhong C. Existence of a global attractors for a p-Laplacian equation in R^N [ J ]. Nonlinear Analysis, 2007, 66:367-399.
  • 8Li Y, Zhong C. Pullback attractor for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equation [ J ]. Applied Mathematics and Computation, 2007, 190:1 020- 1 029.
  • 9Sun C, Zhong C. Attractors for the semilinear reactiondiffusion equation with distribution derivatives in unbounded domains[J]. Nonlinear Analysis, 2005, 63: 49-65.
数学杂志
2010年 第5期

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