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带衰退记忆的抽象发展方程全局吸引子的存在性 被引量：6

Existence of global attractors for abstract evolution equations with fading memory
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摘要 利用一些最新的研究结果,证明了带衰退记忆的抽象发展方程解的全局吸引子的存在性. The existence of global attractors of solutions for abstract evolution equation was discussed by applying some new results and the existence of global attractors of solution semi-group for abstract evolution equation was proved.
作者 汪璇 任利宁
机构地区 西北师范大学数学与信息科学学院 兰州大学数学与统计学院 兰州交通大学数理与软件工程学院
出处 《兰州大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第5期99-102,107,共5页 Journal of Lanzhou University(Natural Sciences)
基金 国家自然科学基金(10771089) 甘肃省自然科学基金(3ZS061-A25-016)资助.
关键词 抽象发展方程 记忆核 全局吸引子 abstract evolution equation memory kernel global attractor
分类号 O175.27 [理学—基础数学] O175.29 [理学—基础数学]
  • 相关文献

参考文献10

  • 1COLEMAN B D, NOLL W. Foundations of linear viscoelasticity[J]. Rev Mod Phys, 1961, 33: 239-249.
  • 2DAFERMOS C M. Asymptotic stability in viscoelasticity[J]. Arch Rational Mech Anal, 1970, 37: 297- 308.
  • 3FABRIZIO M, MORRO A. Mathematical problem in linear viscoelasticity[C]//SLAM Studies in Applied Mathematics. Philadelphia: SLAM, 1992.
  • 4TEMAM R. Infinite dimensional dynamical system in meehanics and physicS[M]. 2nd ed. New York: Spring Verlag,1997.
  • 5AN Y.On the suspension bridge equations and the relevant problems[D].兰州:兰州大学数学与统计学院,2001.
  • 6GIORGI C, RIVERA J E M, PAT4 V. Global at tractors for a semilinear hyperbolicequations in vis coelasticity[J]. J Math Anal Appl, 2001, 260: 83-99.
  • 7PATA V, ZUCCHI A. Attractors for a damped hyperbolic equation with linear memory[J]. Adv Math Sci Appl, 2001,11(2): 505-529.
  • 8MA Qiao-zhen, ZHONG Cheng-kui. Existence of strong global attractors for hyperbolic equation with linear memory[J], Applied Mathematics and Computation, 2004. 157: 745-758.
  • 9钟承奎,牛明飞.关于无穷维耗散非线性动力系统全局吸引子的存在性[J].兰州大学学报（自然科学版）,2003,39(2):1-5. 被引量：6
  • 10MA Qing-feng, WANG Shou-hong, ZHONG Cheng- kui. Necessary and sufficient conditions for the existence of global attractor forsemigroup and application[J]. Indiana University Mathematics Journal, 2002, 51(6): 1 541-1559.

二级参考文献5

  • 1Rbinson James C. Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors [M].Cambridge :Cambridge University Press ,2001.
  • 2Sell George R,You Yuncheng. Dynamics of Evolutionary Equations [M]. New York :Springer, 2002.
  • 3Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics [M]. New York: Springer,1997.
  • 4Hale J K. Asymptatic Behavior of Dissipative Systems[M]. AMS Providence RJ, 1988.
  • 5Ma Q F,Wang Sh H,Zhong C K. Necessary and sufficient conditions for the existence of global attractors for semigroups and applications[J]. Indiana Uni Math J,2002,51(6):1542-1558.

共引文献5

同被引文献63

  • 1COLEMAN B D, NOLL W. Foundations of linear viscoelasticity[J]. Rev Mod Phys, 1961, 33: 239-249.
  • 2DAFERMOS C M. Asymptotic stability in viscoelasticity[J]. Arch Rational Mech Anal, 1970, 37: 297-308.
  • 3FABRIZIO M, MORRO A. Mathematical problem in linear viscoelasticity[C]//SLAM Studies in Applied Mathematics. Philadelphia: SLAM, 1992.
  • 4TEMAM R. Infinite dimensional dynamical system in mechanics and physics[M]. 2 nd ed. New York: Spring-Verlag, 1997.
  • 5AN Yu-kun. On the suspension bridge equations and the relevant problems[D].兰州:兰州大学数学与统计学院,2001.
  • 6GIORGI C, RIVERA J E M, PATA V. Global attractors for a semilinear hyperbolic equations in viscoelasticity[J]. J Math Anal Apply 2001,260: 83-99.
  • 7PATA V, ZUCCHI A. Attractors for a damped hyperbolic equation with linear memory[J]. Adv Math Sci Appl, 2001, 11(2): 505-529.
  • 8MA Qiao-zhen, ZHONG Cheng-kui. Existence of strong global attractors for hyperbolic equation with linear memory[J]. Applied Mathematics and Computation, 2004, 157- 745-758.
  • 9ZHONG Cheng-kui, YANG Mei-hua, SUN Chun-you. The existence of global attractors for the norm-toweak continuous semigroup and its application to the nonlinear reaction-diffusion equations[J]. J Differential Equations, 2006, 223: 367-399.
  • 10MA Qing-feng, WANG Shou-hong, ZHONG Chengkui. Necessary and sufficient conditions for the existence of global attractor for semigroup and application[J]. Indiana University Mathematics Journal, 2002, 51(6): 1541-1 559.

引证文献6

二级引证文献10

兰州大学学报（自然科学版）
2008年 第5期

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