| 具有粘弹性和热粘弹性方程组的全局周期吸引子 |
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| 引用本文： | 李红艳,陈双全,周盛凡. 具有粘弹性和热粘弹性方程组的全局周期吸引子[J]. 系统科学与数学, 2008, 28(10): 1275-1282 |
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| 作者姓名： | 李红艳 陈双全 周盛凡 |
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| 作者单位： | 1. 上海工程技术大学管理学院,上海,201620
2. 上海师范大学数学系,上海,200234 |
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| 基金项目： | 国家自然科学基金，上海市科委科技攻关重点项目，上海高校选拔培养优秀青年教师基金，校重点学科(XK0704)资助课题 |
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| 摘 要： | 证明了具有粘弹性和热粘弹性方程组在Dirichlet边界条件下,对于任意的非自治时间周期受迫力,均具有唯一的指数吸引任何有界集的周期解,即全局周期吸引子.并且如果受迫力是自治的,则全局周期吸引子恰是系统唯一的指数吸引有界集的平衡解.
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| 关 键 词： | 全局周期吸引子 粘弹性 热粘弹性 |
| 收稿时间： | 2006-04-11 |
| 修稿时间： | 2006-12-25 |
Global Periodic Attractor of Viscoelastic and Thermoviscoelastic Equations |
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| LI Hongyan,CHEN Shuangquan,ZHOU Shengfan. Global Periodic Attractor of Viscoelastic and Thermoviscoelastic Equations[J]. Journal of Systems Science and Mathematical Sciences, 2008, 28(10): 1275-1282 |
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| Authors: | LI Hongyan CHEN Shuangquan ZHOU Shengfan |
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| Affiliation: | (1)School of Management Studies, Shanghai University of Engineering Science, Shanghai 201620; (2)Department of Mathematics, Shanghai Normal University, Shanghai 200234. |
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| Abstract: | The viscoelastic and thermoviscoelastic equations with homogeneous Dirichlet boundary conditions are considered. It is shown that with any nonautonomous and time-periodic driving force, the system has a unique periodic solution attracting any bounded set exponentially, i.e. the global periodic attractor. Moreover, it is proven that the global periodic attractor is the unique equilibrium solution which attracts any bounded set exponentially when the driving force is autonomous. |
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| Keywords: | Global periodic attractor viscoelasticity thermoviscoelasticity. |
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