J4 ›› 2010, Vol. 45 ›› Issue (12): 67-74.

• Articles • Previous Articles     Next Articles

Existence of attractors for the non-autonomous viscoelastic rod equations with memory

WANG Xuan1,2, MA Qiao-zhen1   

  1. 1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070， Gansu, China;
    2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China
  • Received:2009-12-10 Online:2010-12-16 Published:2011-03-16
  • About author:WANG Xuan(1973-), Femal, Associate professor, Ph.D. candidate, her research mainly focuses on applied differential equations and infinite dimensional dynamical systems. Email: wangxuan@nwnu.edu.cn
  • Supported by:

    Supported by the National Natural Science Foundation of China(10871060, 10771089)

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Abstract:

The long-time dynamical behavior of the non-autonomous viscoelastic rod equations with memory is discussed in this paper. Based on some new results and energy estimates, the uniformly decay estimate is obtained. When the forcing term f only satisfies condition (C*) instead of translation compact, the existence of uniform attractors in Vθ×H×L2μ (R+;Vθ) is proven, which extends and improves some known results.

Key words: non-autonomous viscoelastic rod equation; uniform attractor; memory kernel

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