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带衰退记忆的抽象发展方程强全局吸引子的存在性 被引量：4

Existence of strong global attractors for abstract evolution equation with fading memory
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摘要 利用一些最新结果,证明了带衰退记忆的抽象发展方程在强拓扑空间D(A~θ)×V_θ×L_μ~2(R^+;D(A~θ))中全局吸引子的存在性。 The existence of global attractors of solutions for abstract evolution equations was proven in the strong topological space D（A^θ）×Vθ×Lμ^2（R^＋;D（A^θ））by applying some new results.
作者 汪璇 钟承奎
机构地区 西北师范大学数学与信息科学学院 南京大学数学系
出处 《兰州大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第1期113-118,共6页 Journal of Lanzhou University(Natural Sciences)
基金 国家自然科学基金项目(10771089 10871160)
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11

  • 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.
  • 9汪璇,任利宁.带衰退记忆的抽象发展方程全局吸引子的存在性[J].兰州大学学报（自然科学版）,2008,44(5):99-102. 被引量：6
  • 10ZHONG 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.

二级参考文献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.
  • 9MA 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.
  • 10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

共引文献5

同被引文献41

  • 1Giorgi C, Rivera J E M, Pata V. Global attractors for a semilinear hyperbolic equations in viscoelasticity[J]. J. Math. Anal. Appl., 2001,260:83-99.
  • 2Teman R. Infinite Dimensional Dynamical System in Mechanics and Physics[M]. 2nd ed. New York: Spring- Verlag, 1997.
  • 3Pata V, Zucchi A. Attractors for a damped hyperbolic equation with linear memory[J]. Adv. Math. Sci. Appl., 2001:11-505-529.
  • 4Ma Qingfeng, Wang Shouhong, Zhong Chengkui. Necessary and sufficient conditions for the existence of global attractor for semigroup and application[J]. Indiana University Mathematics Journal, 2002,51:1541- 1559.
  • 5Ma Qiaozhen, Zhong Chengkui. Existence of strong global attractors for hyperbolic equation with linear memory[J]. Applied Mathematicsand Computation, 2004,157:745-758.
  • 6Ghidaglia J M, Temam R. Attractors for damped nonlinear hyperbolic equations[J]. J. math. pures Appl., 1987,66:273-319.
  • 7熊明.一类二阶奇异边值问题的正解[J].西南大学学报（自然科学版）,2007,29(8):43-48. 被引量：9
  • 8GIORGI C, RIVERA J E M, PATA V. Global attractors for a semilinear hyperbolic equations in viscoelasticity[ J ] J Math Anal Appl , 2001, 260: 83-99.
  • 9TEMAM R. Infinite Dimensional Dynamical System in Mechanics and Physics [ M]. Second edition. Berlin: Springer-Verlag, 1997.
  • 10PATA V, ZUCCHI A. Attractors for a damped hyperbolic equation with linear memory [ J ]. Adv Math SciAppl, 2001, 11(2): 505-529.

引证文献4

二级引证文献9

兰州大学学报（自然科学版）
2010年 第1期

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