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exponential attractor FOR THE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATION WITH DAMPING TERM

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Applied Mathematics and Mechanics(English Edition) 2005年第3期26卷 283-291页

作者：尚亚东郭柏灵 School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510405 P.R.China Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 P.R.China

The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence... 详细信息

关键词： symmetric regularized long wave equation asymptotic behavior squeezing property exponential attractor

exponential attractor for a Nonlinear Boussinesq Equation

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Acta Mathematicae Applicatae Sinica 2006年第3期22卷 443-450页

作者： Ahmed Y. Abdallah Departmcnt of Mathematics University of Jordan Amman 11942 Jordan

This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H0^2（0, 1） × L^2（0, 1）. The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H0^3（0, 1） × H0^1（0, 1）.

关键词： Boussinesq equation absorbing set exponential attractor

exponential attractor for Davey-Stewartson Equation in a Banach Space

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Journal of Mathematical Research and Exposition 2005年第3期25卷 391-398页

作者：黄健戴正德云南大学数学系云南昆明650091

In this paper, the existence of the exponential attractor of Davey-Stewartson equation is considered and its estimation of fractal dimension is obtained in a Banach subspace Xp^α of L^p（Ω）.

关键词： Davey-Stewartson equation exponential attractor Banach space.

exponential attractors for the Generalized Ginzburg-Landau Equation

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Acta Mathematica Sinica,English Series 2000年第3期16卷 515-526页

作者： Boling Guo Institute of Applied Physics and Computational Mathematics P.O.Box 8009,Beijing,100088,P.R.ChinaBixiang Wang Department of Mathematics,Brigham Young University,Provo,UT84602,USA Institute of Applied Physics and Computational Mathematics Bejing 100088 P. R. China Department of Mathematics Brigham Young University Provo UT 84602 USA

In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial *** show the squeezing property and the existence of fimte dimen- sional exponential attractors for this e... 详细信息

关键词： Global attractor exponential attractor Semigroup Ginzburg-Landau equation

exponential attractorS OF THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

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Acta Mathematicae Applicatae Sinica 2001年第4期17卷 484-493页

作者：戴正德蒋慕蓉 Department of Mathematics Yunnan University Kunming China

In this paper, the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.

关键词： exponential attractor Ginzburg-Landau-BBM equations unbounded domain weighted function squeezing property

exponential attractors for the Ginzburg-Landau-BBM Equations

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Journal of Mathematical Research and Exposition 2001年第3期21卷 317-322页

作者：戴正德蒋慕蓉云南大学数学系昆明650091

In this paper, the existence of the exponential attractors for the Ginzburg- Landau-BBM equations with periodic initial and boundary conditions are obtained by using the squeezing property and the operator dccompositi... 详细信息

关键词： exponential attractor Ginzburg-Landau-DBM equatious squeezing prop- erty.

LONG-TIME BEHAVIOR FOR A THERMOELASTIC MICROBEAM PROBLEM WITH TIME DELAY AND THE COLEMAN-GURTIN THERMAL LAW

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Acta Mathematica Scientia 2021年第2期41卷 609-632页

作者： Wenjun LIU Dongqin CHEN Zhijing CHEN School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China

This study addresses long-time behavior for a thermoelastic microbeam problem with time delay and the Coleman-Gurtin thermal law,the convolution kernel of which entails an extremely weak dissipation in the thermal *** using the semigroup theory,we first establish the existence of global weak and strong solutions as well as their continuous dependence on the initial data in appropriate function spaces,under suitable assumptions on the weight of time delay term,the external force term and the nonlinear *** then prove that the system is quasi-stable and has a gradient on bounded variant sets,and obtain the existence of a global attractor whose fractal dimension is finite.A result on the exponential attractor of the system is also proved.

关键词： Microbeam problem time delay Coleman-Gurtin law global attractor exponential attractor

Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

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Engineering（科研） 2023年第10期15卷 632-646页

作者： Suping Wang Qiaozhen Ma Xukui Shao School of Mathematics and Information Engineering Longdong University Qingyang China School of Mathematics and Statistics Northwest Normal University Lanzhou China

This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.

关键词： Suspension Bridge Equation State-Dependent Delay Global attractor exponential attractor Quasi-Stability