带有记忆核的可拉伸时滞吊桥方程解的长时间行为（英文）

吊桥方程解的长期动力学行为已有许多经典结论,但关于时滞吊桥方程动力学行为的研究甚少.本文研究带有记忆核的可拉伸时滞吊桥方程解的长期动力学行为,利用压缩函数的方法,获得该时滞吊桥方程拉回吸引子的存在性.     

带有非齐次结构动力因子模型的估计与检验

因子模型在刻画因子之间的相互关系以及因子与观测变量之间的关联性具有重要作用.在实际应用中,观测数据往往呈现出时序变异多峰、偏态等特性.本文将经典的潜变量模型延伸到非齐次隐马尔可夫潜变量模型,建立了极大似然统计分析程序.经验结果展示所建立的统计程序是有效的.     

流态化非均匀结构的概率模型

通过对实验数据的直方图的分析和统计检验的手段,找到了定量描述一类气固流化订系统非均匀结构动态行淡的概率分布－七参娄威布尔分布,提示了这种复杂系统内非均匀性的一些规律,模拟结果是理想的。     

具衰退记忆的四阶拟抛物方程的长时间行为

该文主要研究带衰退记忆和临界非线性的四阶拟抛物方程的长时间行为.在过去历史框架下,利用解算子半群的分解技巧和紧性转移定理证明了对应的动力系统的整体吸引子存在性.     

非守恒相场模型长时间行为的一个注记

本文讨论了一类非守恒相场模型解的长时间行为,证明了当ｔ→∞时,对任意ｍ≥１,解在Ｃ＾ｍ（Ω）中收敛于对应稳态问题的解。     

带有多项式非线性项的高维反应扩散方程有限差分格式的长时间行为

本文考虑了一类带有多项式非线性项的高维反应扩散方程．建立了一个全离散的有限差分格式,并证明了差分解的存在唯一性．分析了由差分格式生成的离散系统的动力性质,在对差分解先验估计的基础上得到了离散动力系统的整体吸引子的存在性．最后证明了差分格式的长时间稳定性和收敛性．     

一类带有非均匀项的广义KdV方程的孤波解

一类带有非均匀项的广义ＫｄＶ方程的孤波解朱佐农（扬州大学农学院基础部，扬州２２５Ｏ０１）－、引言众所周知，ＫｄＶ方程已被广泛研究［１］．从方程（１）的高阶守恒量出发，Ｌａｘ得到第一族高阶ＫｄＶ方程，其５阶形式为：从（２）的守恒量出发，Ｓａｗａｄａ和Ｋ...     

带有定性因素均匀设计的均匀性度量准则

我们在文〔3〕中曾讨论了如何用均匀设计来安排含有定性因素的试验。在文〔1〕中所使用的均匀设计表是针对试验中全为连续因素设计的。显然 ,当试验中含有定性因素时 ,均匀性的度量和相应均匀设计表的设计都会有所不同。这是一个值得研究的课题。本文主要探讨均匀性的度量 ,并用文中提出的准则 ,对文〔1〕中一些均匀设计表的均匀性给出了数值性结果     

非均匀变截面梁动力响应的一般解

本文利用精确解析法[1]给出非均匀变截面梁在任意谐振荷载和边界条件下的动力响应的一般解.问题最后归结为求解一个非正定微分方程.对于这一问题用一般变分法求解失败,利用本文的方法,这个问题的一般解可以写成解析的形式.因此对优化特别方便.本文给出收敛性证明.文末给出的算例表明本文的方法可获得满意的结果.     

一类多维非齐次GBBM方程初边值问题解的长时间行为

研究一类多维非齐次广义Benjamin-Bona-Mahony(GBBM)方程的初值边界问题,利用Sobolev插值不等式,做关于时间的一致性先验估计,证明该问题的整体吸引子的存在性．     

Global Dynamics of a Nonlinear Beam Equation with Strong Structural Damping

In this paper, the global attractor, exponential attractor and flat inertial manifold are obtained for a nonlinear beam equation with strong structural damping.     

具有双记忆项的热弹耦合梁方程的整体吸引子

研究了具有双记忆项的非线性热弹耦合梁方程,利用已知的研究结果给出解的适定性定理,其次通过先验估计并结合常用不等式证明系统存在有界吸收集,且利用标准方法验证半群的渐近紧性,得到整体吸引子的存在性.     

Long-time dynamics for a nonlinear Timoshenko system with delay

This paper is concerned with a nonlinear Timoshenko system with a time delay term in the internal feedback together with initial data and Dirichet boundary conditions. Under some suitable assumptions on the weights of feedback, we obtain the existence of a global attractor with finite fractal dimension for the case of equal speed wave propagation. Furthermore, the existence of exponential attractors is also derived.     

具有非线性记忆项的耗散波动方程的整体吸引子

LetΩRn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt+αut-△u-∫0t 0μ(t-s)|u(s)| βu(s)ds + g(u)=f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10(Ω)×L2(Ω).     

具有时滞的双向联想记忆(BAM)的神经网络的全局动力学行为

在没有假定关联函数的光滑性,单调性和有界性的条件下,应用Liapunov泛函方法和矩阵代数技术,得到具有常数传输时滞的双向联想记忆(BAM)的神经网络模型平衡点存在性和全局指数稳定性的一些新的充分条件,这些条件可以由网络参数,连接矩阵和关联函数的Lipschitz常数所表示的M矩阵来刻化．这些结果不仅是简单和实用的,而且相对于已有文献的结果具有较少的限制和更易于验证．     

Global Dynamics of the Oregonator System

In this work, the existence and properties of a global attractor for the solution semiflow of the Oregonator system are proved. The Oregonator system is the mathematical model of the celebrated Belousov–Zhabotinskii reaction. A rescaling and grouping estimation method is developed to show the absorbing property and the asymptotic compactness of the solution trajectories of this three‐component reaction–diffusion system with quadratic nonlinearity. It is also proved that the fractal dimension of the global attractor is finite and an exponential attractor exists for the Oregonator semiflow. Copyright © 2012 John Wiley & Sons, Ltd.     

Trajectory attractors for nonclassical diffusion equations with fading memory

In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7,8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.     

Long-time behavior for a nonlinear plate equation with thermal memory

We consider a nonlinear plate equation with thermal memory effects due to non-Fourier heat flux laws. First we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we use a suitable ?ojasiewicz-Simon type inequality to show the convergence of global solutions to single steady states as time goes to infinity under the assumption that the nonlinear term f is real analytic. Moreover, we provide an estimate on the convergence rate.     

Stability of global and exponential attractors for a three‐dimensional conserved phase‐field system with memory

We consider a conserved phase‐field system on a tri‐dimensional bounded domain. The heat conduction is characterized by memory effects depending on the past history of the (relative) temperature ?, which is represented through a convolution integral whose relaxation kernel k is a summable and decreasing function. Therefore, the system consists of a linear integrodifferential equation for ?, which is coupled with a viscous Cahn–Hilliard type equation governing the order parameter χ. The latter equation contains a nonmonotone nonlinearity ? and the viscosity effects are taken into account by a term ?αΔ?_tχ, for some α?0. Rescaling the kernel k with a relaxation time ε>0, we formulate a Cauchy–Neumann problem depending on ε and α. Assuming a suitable decay of k, we prove the existence of a family of exponential attractors {?_α,ε} for our problem, whose basin of attraction can be extended to the whole phase–space in the viscous case (i.e. when α>0). Moreover, we prove that the symmetric Hausdorff distance of ?_α,ε from a proper lifting of ?_α,0 tends to 0 in an explicitly controlled way, for any fixed α?0. In addition, the upper semicontinuity of the family of global attractors {??_α,ε} as ε→0 is achieved for any fixed α>0. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.