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GEVREY CLASS REGULARITY AND approximate inertial manifoldS FOR THE NEWTON-BOUSSINESQ EQUATIONS

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Chinese Annals of Mathematics,Series B 1998年第2期19卷 179-188页

作者： GUO BOLING WANG BIXIANG Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China Department of Applied Mathematics Tsinghua University Beijing 100084 China

The authors show the Gevrey class regularity of the solutions for the two-dimensional Newton-Boussinesq Equations. Based on this fact, an approximate inertial manifold for the system is constructed, which attracts ... 详细信息

关键词： Gevrey class regularity Global attractor approximate inertial manifold Newton-Boussinesq Equation

CONVERGENT FAMILIES OF approximate inertial manifoldS FOR NONAUTONOMOUS EVOLUTION EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 1998年第8期19卷 765-775页

作者：王宗信范先令朱正佑 Institute of Mathematics Fudan University Shanghai P. R. China Department of Mathematics Lanzhou University Lanzhou P. R. China Department of Mathematics Shanghai University Shanghai P. R. China

In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is studied. A family of convergent approximate inertial manifolds for a class of evolution equations has been constructed w... 详细信息

关键词： nonautonomous equation approximate inertial manifold spectral gap condition

On the construction of approximate inertial manifolds

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Journal of Mathematical Research with Applications 1995年第3期 367-368页

作者： Wang Bixiang(Dept. of Math., Lanzhou University, Lanzhou 730000)

ＯｎｔｈｅＣｏｎｓｔｒｕｃｔｉｏｎｏｆＡｐｐｒｏｘｉｍａｔｅＩｎｅｒｔｉａｌＭａｎｉｆｏｌｄｓＷａｎｇＢｉｘｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ７３００００）Ｏｎｔｈ... 详细信息

ＯｎｔｈｅＣｏｎｓｔｒｕｃｔｉｏｎｏｆＡｐｐｒｏｘｉｍａｔｅＩｎｅｒｔｉａｌＭａｎｉｆｏｌｄｓＷａｎｇＢｉｘｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ７３００００）ＯｎｔｈｅＣｏｎｓｔｒｕｃｔｉｏｎｏｆＡｐ...

关键词： contraction principle approximate inertial manifold reaction diffusion equa-tion.

Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation

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Acta Mathematica Sinica,English Series 2002年第3期18卷 579-596页

作者： Bo Ling GUO Bi Xiang WANG Institute of Applied Physics and Computational Mathematics, P. O. Box 8009. Beijing 100088. P. R. China Institute of Applied Physics and Computational Mathematics Beijing P. R. China

In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system.

关键词： Global solution approximate inertial manifold Gevrey class regularity Kolmogorov-Spiegel-Sivashinsky equation

WAVELET BASIS ANALYSIS IN PERTURBEDPERIODIC KdV EQUATION

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Applied Mathematics and Mechanics(English Edition) 1998年第11期19卷 0-0,0-0+0-0页

作者：卢殿臣田立新刘曾荣 Department of Mathematics and Physics Jiangsu University of Science and Technology Zhenjiang P.R. China Department of Mathematics Shanghai University Shanghai P.R. China

In the paper by using the spline wavelet basis to constructr the approximate inertial manifold, we study the longtime behavior of perturbed perodic KdV equation.

关键词： wavelet basis approximate inertial manifold perturbed periodic KdV equation

Numerical Simulation of Weakly Damped force KdV Eqation

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Communications in Nonlinear Science and Numerical Simulation 1996年第3期1卷 42-45页

作者： Lixin TIAN Nailong GUO(Department of Mathmatics and Physics,Jiangsu University of Science and technology,Zhenjhag 212013, Jiangsu, P.R.China.) Department of Mathmatics and Physics Jiangsu University of Science and technology Zhenjiang 212013 Jiangsu P.R. China

In this paper we set approximate inertial manifold of weakly damped forcedKdV equation and get the numerical simulation. The result using the method is as sameas the numerical simulation.

关键词： approximate inertial manifold weakly dampled forced KdV equation selfadjoint operator

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS　

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Applied Mathematics(A Journal of Chinese Universities) 1994年第1期9卷 11-30页

作者： LIKAITAI HEYINNIAN XIANGYIMIN InstituteofComputationalandAppliedMathematics Xi＇anJiaotongUniversityXi＇an710049 InstituteofComputationalandAppliedMathematics Xi＇anJiaotongUniversityXi＇an710049

This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the erro... 详细信息

关键词： Full Discrete Nonlinear Galerkin Method Fractional Step Method approximate inertial manifold Navier-Stokes Equations.AMS Subject Classification.65N30 65M60.

THE RESEARCH OF LONGTIME DYNAMIC BEHAVIOR IN WEAKLY DAMPED FORCED KdV EQUATION

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Applied Mathematics and Mechanics(English Edition) 1997年第10期18卷 0-0,0-0+0-0+0-0页

作者：徐振源田立新

It is presented that there exists approximate inertial manifolds in weakly damped forced Kdv equation with with periodic boundary conditionsIIbns. The approximate inertial manifolds provide approximant of the attractror by finite dimensional smooth manifolds which are exphcitly defined And the concepl leads to new numerical schemes which are well adapted to the longtime behavior of dynamical system.

关键词： approximate inertial manifold weakly damped forced KdV equation dynamical system attractor

A SIMPLE POSTPROCESS PROCEDURE FOR GALERKIN METHOD

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Applied Mathematics and Mechanics(English Edition) 2000年第1期21卷 81-88页

作者：侯延仁李开泰

A kind simple postprocess procedure for classical Galerkin method for steady Navier_Stokes equations with stream function form was presented in this paper. The main ideal was to construct an approximate interactive rule between lower frequency components and higher frequency components by using the conception of approximate inertial manifold(AIM) and a kind of new decomposition of the true solution. It is demonstrated in this paper that this kind of postprocess Galerkin method could derive a higher accuracy solution with lower computing efforts.

关键词： Navier_Stokes equations approximate inertial manifold non_singular solution