带记忆的非自治黏弹性棒方程的吸引子的存在性

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

带记忆的非自治黏弹性棒方程的吸引子的存在性

汪璇^1,2,马巧珍¹

1. 西北师范大学数学与信息科学学院, 甘肃兰州 730070;
2. 兰州大学数学与统计学院, 甘肃兰州 730000

收稿日期:2009-12-10 出版日期:2010-12-16 发布日期:2011-03-16

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

WANG Xuan^1,2, MA Qiao-zhen¹

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)

摘要/Abstract

摘要：

讨论了带衰退记忆的半线性非自治黏弹性棒方程的长时间动力学行为。通过应用一些新的结果和能量估计技巧,获得了能量的一致衰退估计，当外力项满足(C*)条件而非平移紧时, 证明了一致吸引子在V_θ×H×L²_μ (R⁺;V_θ)上的存在性, 此结果推广和改进了一些已有结果。

关键词: 非自治黏弹性棒方程; 一致吸引子; 记忆核

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 V_θ×H×L²_μ (R⁺;V_θ) is proven, which extends and improves some known results.

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

汪璇1,2,马巧珍1. 带记忆的非自治黏弹性棒方程的吸引子的存在性[J]. J4, 2010, 45(12): 67-74.

WANG Xuan1,2, MA Qiao-zhen1. Existence of attractors for the non-autonomous viscoelastic rod equations with memory[J]. J4, 2010, 45(12): 67-74.

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