Neumann边界条件下强阻尼波动方程的一维全局吸引子

本文主要考虑齐次Neumann边界条件下强阻尼波动方程的全局吸引子的存在性．利用渐近时间周期微分方程的极限集的性质,证明了在一定的参数范围内,齐次Neumann边界条件下强阻尼波动方程存在一维全局吸引子,是一条水平曲线．     

相对论弦振动方程带Neumann边界条件的初边值问题（英文）

相对论弦振动方程带非齐次Neumann边界条件的混合初边值问题在弦理论和粒子物理学中有着重要作用.研究了第一象限内该类方程带有Neumann边界条件的混合初边值问题,在一定的初边值条件下,得到了经典解的整体存在性和唯一性.     

关于具间接阻尼的强耦合波动方程组的边界耗散传输的敏感性

本文考察由两个强耦合的波动方程组成的间接边界阻尼反馈系统的稳定性,阐明此类系统的稳定性依赖于耦合的类型、无阻尼系统是否有隐含正则性、以及边界耗散的阶数和无阻尼边界条件间的匹配等诸多因素.首先证明,当无阻尼边界为Dirichlet边界条件时,系统是一致指数稳定的;而当其为Neumann边界条件时,只能建立系统的多项式稳定性.其次,通过谱分析的方法,揭示间接边界阻尼反馈系统的能量在方程间的传递与无阻尼边界条件之间的内在联系.     

强阻尼半线性波动方程的全局吸引子

本文讨论一类带强阻尼项的半线性波动方程的全局吸引子的存在性．首先给出了方程解的存在唯一性定理，建立了解的C°-半群；然后运用Hale提出的a-收缩理论，证明了该类方程存在全局吸引子．     

一类非线性波动方程弱解的存在唯一性

在考虑强阻尼效应的情形下,建立了一类轴向载荷作用下的波动方程.研究一类具有强阻尼的非线性波动方程的初边值问题的整体解的性态.以Sobolev空间的性质为工具,利用Faedo-Galerkin方法,证明了该方程在线性边界条件下弱解的存在唯一性,为力学中具有阻尼结构的振动问题的研究提供了重要依据.     

Neumann边界条件下离散化强阻尼Sine-Gordon方程的全局吸引性

本文主要研究Neumann边界条件下带有周期外力的离散化强阻尼Sine-Gordon方程的全局吸引性.当摩擦系数足够大时,该系统将拥有一族周期解,这些周期解彼此之间只相差-个常向量的整数倍,并且该系统的任意一个解都将被其中的-个周期解所吸引.     

非齐次边界条件下Sine-Gordon型二阶非线性系统的全局吸引子及能稳性

本文在非齐次边界条件下,证明了有阻尼Sine-Gordon型二阶非线性系统的全局吸引子的存在性．同时证明了当时,该全局吸引子为—个平衡点,而且该平衡点具有指数吸引性．并将所得结果应用到系统能稳性的研究中．     

具有Holling-Ⅲ型功能反应的捕食者-食饵扩散模型中避难所的影响

本文在齐次Neumann边界条件下考虑食饵具有避难所的捕食者-食饵扩散模型,其功能反应函数为Holling-III型.主要讨论该系统全局吸引子的存在性和系统永久持续生存性,以及避难所对系统非负平衡点稳定性的影响.     

具有Holling-III型功能反应的捕食者-食饵扩散模型中避难所的影响

本文在齐次Neumann边界条件下考虑食饵具有避难所的捕食者-食饵扩散模型, 其功能反应函数为Holling-III 型. 主要讨论该系统全局吸引子的存在性和系统永久持续生存性, 以及 避难所对系统非负平衡点稳定性的影响.     

关于耗散波动方程精确能控性的奇异极限的一个注记

本文在比文献［１］更一般的几何控制条件下，分析了具齐次Ｄｉｒｉｃｈｌｅｔ边界条件的耗散波动方程精确能控性的奇异摄动问题．结论是由这类波动方程的精确能控性可得到热传导方程的精确零能控性．     

非线性Sobolev-Galpern方程的有限维整体吸引子

本文研究非线性Sobolev-Galpern方程解的渐近性态．首先证明了该方程在H^2(Ω)∩H0^1(Ω)中整体弱吸引子的存在性，然后利用一个能量方程证明了整体弱吸引子实际上是整体强吸引子，建立了整体吸引子的有限维性．     

Attractors for the Long-short Wave Equations

In the present paper, we study the long time behaviour of solutions for the long-short wave equations with zero order dissipation. We first construct the global weak attractor for this system in H²_{per} × H¹_{per}. And then by exact analysis of two energy equations, we show that the global weak at attractor is actually the global strong attractor in H²_{per}.     

Large-time behavior of solutions to degenerate damped hyperbolic equations

We investigate the asymptotic behavior of solutions to damped hyperbolic equations involving strongly degenerate differential operators. First we establish the existence of a global attractor for the damped hyperbolic equation under consideration. Then we prove the finite dimensionality of the global attractor.     

KdV-Burgers-Kuramoto系统的渐近吸引子

研究了 KdV-Burgers-Kuramoto 方程的渐近吸引子,即利用正交分解法构造一个有限维解序列。首先用数学归纳法证明了该解序列不会远离方程的整体吸引子,接着证明解序列在长时间后无限趋于方程的整体吸引子,最后给出渐近吸引子的维数估计。     

Attractors and dimension of dissipative lattice systems

In this paper, by using the argument in [Q.F. Ma, S.H. Wang, C.K. Zhong, Necessary and sufficient conditions for the existence of global attractor for semigroup and application, Indiana Univ. Math. J., 51(6) (2002), 1541-1559.], we prove that the condition given in [S. Zhou, Attractors and approximations for lattice dynamical systems, J. Differential Equations 200 (2004) 342-368.] for the existence of a global attractor for the semigroup associated with general lattice systems on a discrete Hilbert space is a sufficient and necessary condition. As an application, we consider the existence of a global attractor for a second-order lattice system in a discrete weighted space containing all bounded sequences. Finally, we show that the global attractor for first-order and partly dissipative lattice systems corresponding to (partly dissipative) reaction-diffusion equations and second-order dissipative lattice systems corresponding to the strongly damped wave equations have finite fractal dimension if the derivative of the nonlinear term is small at the origin.     

Parameterizing the global attractor of the navier-stokes equations by nodal values

In this paper we give an affirmative answer to the conjecture of Foias and Tern am that the elements of the global attractor of the two dimensional Navier Stokes equations are uniquely determined by their nodal values at a finite number of points in the underlying physical domain. This is kind of a sampling theorem for the elements of the the global attractor of the Navier Stokes equations.     

On global attractors of the 3D Navier-Stokes equations

In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with respect to two topologies—weak and strong. Each such system possesses a global attractor in the weak topology, but not necessarily in the strong. In case the latter exists and is weakly closed, it coincides with the weak global attractor. We give a sufficient condition for the existence of the strong global attractor, which is verified for the 3D NSE when all solutions on the weak global attractor are strongly continuous. We also introduce and study a two-parameter family of models for the Navier-Stokes equations, with similar properties and open problems. These models always possess weak global attractors, but on some of them every solution blows up (in a norm stronger than the standard energy one) in finite time.     

Random attractor for the three-dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise

The aim of this article is to study the asymptotical behavior, in terms of upper semi-continuous property of attractor, for small multiplicative noise of the three-dimensional planetary geostrophic equations of large-scale ocean circulation. In this article, we establish the existence of a random attractor for the three-dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise by verifying the pullback flattening property and prove that the random attractor of the three-dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise converges to the global attractor of the unperturbed three-dimensional planetary geostrophic equations of large-scale ocean circulation when the parameter of the perturbation tends to zero.     

THE LONG-TIME BEHAVIOR OF SPECTRAL APPROXIMATE FOR KLEIN-GORDON-SCHROEDINGER EQUATIONS

Klein-Gordon-Schroedinger (KGS) equations are very important in physics. Some papers studied their well-posedness and numerical solution [1-4], and another works investigated the existence of global attractor in R^n and Ω包含于R^n (n≤3) [5-6,11-12]. In this paper, we discuss the dynamical behavior when we apply spectral method to find numerical approximation for periodic initial value problem of KGS equations. It includes the existence of approximate attractor AN, the upper semi-continuity on A which is a global attractor of initial problem and the upper bounds of Hausdorff and fractal dimensions for A and AN,etc.