非局部Kuramoto-Sivashinsky方程整体吸引子的维数估计

本文主要讨论NK-S方程整体吸引子的Hausdorff维数的上界估计.     

弱阻尼广义KdV方程的整体吸引子

证明了具有弱阻尼项的广义KdV方程约周期初边值问题解的存在唯—性及整体吸引子存在性,最后获得了吸引子的Hausdorff维数和分形维数的上界估计．     

非线性光学中薛定谔型方程的整体吸引子

研究了一类非线性薛定谔型方程,描述了光波在光折射晶体中的传播.首先构造了该模型整体弱的吸引子,然后通过能量方程的精确分析,证明整体弱吸引子实际为系统整体强吸引子.最后给出了整体吸引子的分形维数和Hausdorff维数的上界估计.     

广义耦合FitzHugh-Nagumo方程解的渐近行为

本文研究了广义耦合FitzHugh—Nagumo方程及广义离散耦合FitzHugh-Nagumo方程，分别证明了连续模型及离散模型整体吸引子的存在性，并给出了其Huasdorff维数估计，其中离散模型的Hausdorff维数上界与n无关．     

非自治的Schrdinger方程的吸引子

研究2维的非自治非线性Schrdinger方程长时间的动力学行为,证明了一致吸引子的存在性,并给出了该一致吸引子Hausdorff维数的上界,     

非自治的Schroedinger方程的吸引子

研究2维的非自治非线性Schroedinger方程长时间的动力学行为。证明了一致吸引子的存在性,并给出了该一致吸引子Hausdorff维数的上界。     

非自治的Schrdinger方程的吸引子

研究 2维的非自治非线性Schr dinger方程长时间的动力学行为·　证明了一致吸引子的存在性 ,并给出了该一致吸引子Hausdorff维数的上界·     

耗散的广义对称正则长波方程周期初值问题的整体吸引子

该文考虑了带有耗散项的广义对称正则长波方程解的长时间性态.证明了周期初值问题整体吸引子的存在性,用关于时间的一致先验估计获得整体吸引子的Hausdorff和分形维数的上界估计.     

非光滑区域上非自治Navier-Stokes 方程非齐边界问题的吸引子

本文研究在2维Lipschitz区域上Navier-Stokes方程的非齐边界问题的长时间行为，在外力是时间的拟周期下，通过引入双参过程的概念，证明一致吸引子A的存在性，并给出一致吸引子A的Hausdorff维数的上界估计。     

具阻尼的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计

本文得到了一类具有线性阻尼且非线性项满足临界增长条件的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计．     

迭代函数系统的吸引子的维数估计

某些迭代函数系统（ＩＦＳ）的吸引子的Ｈａｕｓｄｏｒｆ维数的经典估计通常由求解两个非线性方程的解得到．在相同条件下，本文给出了一些显式不等式估计，使经典估计是其中的特殊情形．而且某些ＩＦＳ的吸引子的维数可以通过求解满足一定条件的非线性方程而得出     

The Global Attractors for the Dissipative Generalized Hasegawa-Mima Equation

The long time behavior of solutions of the generalized Hasegawa-Mima equation with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimate of the upper bound of the Hausdorff and fractal dimensions for the global attractors is obtained by means of uniform a priori estimates method.     

Global attractors for the initial value problems of Cohn-Hilliard equations on compact manifolds

In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.     

Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term

In this paper we consider a semi-dicretized nonlinear Schrödinger (NLS) equation with local integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained, and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments are given and many interesting phenomena are observed such as limit cycles, chaotic attractors and a so-called crisis of the chaotic attractors.     

Global attractor for the nonlinear strain waves in elastic waveguides

1. IntroductionIn some problems of nonlinear wave propagation in waveguides, the illteraction of waveguides and the external medium and, therefore, the possibility of energy exchange throughlateral surface of waveguide cannot be neglected. When the energy exchange between therod and the medium is considered, for one cajse, there is a dissipation of deformation wavein the viscous external medium. The general cubic double dispersion equation (CDDE) canbe derived from Hamilton principled]:where…     

ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS

1. IntroductionIn this paper) we consider the following periodic initial value problem for the system ofGinzburg-Landau equation coupled with BBM equationwhere e(x,t) is a complex function, n(x, t) is a real scalar function, at a, 5, 7, al, a2, FI, adZare real constants, and gi (x), g200 are given real functions.This problem describes the nonlinear interactions between Langmuir wave and ion acousticwave in plasma physics, e(x, t) denotes electric field, n(x, t) the perturbation of density (…     

The Global Attractors for the Periodic Initial Value Problem of Generalized Kuramoto-Sivashinsky Type Equations in Multi-dimensions

The existence of global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations in multi-dimensions is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniform priori estimates for time.     

Finite Dimensional Behavior for Weakly Damped Generalized KdV-Burgers Equations

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The Global Attractors for Damped Generalized Coupled Nonlinear Wave Equations

The existence of global attractors for the periodic initial value problem of damped generalized coupled nonlinear wave equations is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniformly priori estimates for time.