| Asymptotic Attractors of the Nonlinear Evolution Equation in Bounded Domain |
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| 作者姓名： | ZHAO Lei-n ZHANG Xing-you XING Ting-li |
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| 作者单位： | 1. College of Mathematics and physis, Chongqing University, Chongqing 400030, China; 2. Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand |
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| 摘 要： | The basic principle of infinite-dimensional dynamic system is to try to reduce the original infinite-dimensional system to an infinite-dimensional system. However,due to the unknown structure of the reduced system, it is difficult to describe its dynamical behaviour. To overcome this difficulty, the idea of approximate inertial manifolds is introduced, for NSE, the existence of AIM was studied, it is shown that the global attractor lies within a neighborhood of the graph of an Lipschitz function by the squeezing property. In this paper, by constructing a finite dimensional solution sequence, we will prove that it tends to the global attractor, theoretically, this provides a metod of constructing the asymptotic attractors, theoretically, this provides a method of constructing the asymptotic attractors for the evolution equations.
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| 关 键 词： | nonlinear evolution equation global attractor asymptotic attractors |
| 修稿时间： | 2006/8/17 0:00:00 |
Asymptotic Attractors of the Nonlinear Evolution Equation in Bounded Domain |
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| ZHAO Lei-n,ZHANG Xing-you,XING Ting-li.Asymptotic Attractors of the Nonlinear Evolution Equation in Bounded Domain[J].Storage & Process,2007(2):136-138148. |
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| Authors: | ZHAO Lei-n ZHANG Xing-you XING Ting-li |
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| Institution: | 1. College of Mathematics and physis, Chongqing University, Chongqing 400030, China; 2. Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand |
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| Abstract: | The basic principle of infinite-dimensional dynamic system is to try to reduce the original infinite-dimensional system to an infinite-dimensional system. However,due to the unknown structure of the reduced system, it is difficult to describe its dynamical behaviour. To overcome this difficulty, the idea of approximate inertial manifolds is introduced, for NSE, the existence of AIM was studied, it is shown that the global attractor lies within a neighborhood of the graph of an Lipschitz function by the squeezing property. In this paper, by constructing a finite dimensional solution sequence, we will prove that it tends to the global attractor, theoretically, this provides a metod of constructing the asymptotic attractors, theoretically, this provides a method of constructing the asymptotic attractors for the evolution equations. |
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| Keywords: | nonlinear evolution equation global attractor asymptotic attractors |
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