一个完全双曲相场系统的指数吸引子

本文研究一个非线性双曲微分积分系统,它由H.G.Rotstein等人于2001年提出,用来描述某种特殊的相位转换现象.该系统刻画了相对温度(?)和序参数(或相场)x的变化规律.对(?)和x分别赋予Dirichlet和Neumann边界条件下,该问题生成一个耗散的动力系统,Grasselli和Pata证明了该系统整体吸引子的存在性,随后,Grasselli证明了该系统的指数吸引集的存在性.本文进一步证明其指数吸引子的存在性,在得到指数吸引子有有限的分形维数的同时得到整体吸引子的分形维数的有限性.     

非线性应变波耦合组的吸引子的正则性

本文研究了非线性应变波方程与Schr(?)dinger方程耦合系统Cauchy问题吸引 子的正则性.获得了该系统在空间Eo中存在整体吸引子Ao,并且Ao与E1中的强吸 引子A1相等.     

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．     

具有温和阻尼的非线性热弹耦合系统的整体吸引子

本文研究有界区域下带有温和阻尼的非线性热弹耦合系统的整体解的适定性和整体吸引子的问题.首先,利用Faedo-Galerkin的方法,证明初边值问题弱解的适定性,其次根据解的适定性构造了动力系统,最后给出系统有界吸收集的存在性和半群的一致紧性,证明了系统整体吸引子的存在性.     

推广的B-BBM方程的整体吸引子和指数吸引子

本文对耗散的推广的B－BBM方程的长时间动力学行为进行了研究，证明了该方程整体吸引子和指数吸引子的存在性。     

Ginzburg—Landau—Newell模型的动力学行为

本文对Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－Ｎｅｗｅｌｌ模型的动力学行为进行了讨论，得到了该模型的整体吸引子的存在性，同时得到了此吸引子维数的下界估计和该吸引子的Ｈａｕｓｄｏｒｆｆ维数和Ｆｒａｃｔａｌ维数的上界估计。     

具有线性乘积白噪声的随机非自治吊桥方程的随机指数吸引子

本文考虑具有线性乘积白噪声的随机非自治吊桥方程长时间行为.首先,建立了所研究共圈系统的适定性;第二步,研究了该系统随机吸引子的存在性;第三步,当随机系数趋于0时,得到了随机吸引子的上半连续性;第四步,通过``迭代''法证明了随机吸引子在高正则空间中的正则性;最后,给出了该系统随机指数吸引子的存在性,同时得到了吸引子的有限分形维数.     

一类耦合梁方程组在非线性边界条件下解的长时间动力行为（英文）

本文研究一类具有强阻尼项的耦合梁方程组在非线性边界条件下的长时间动力行为,首先利用一些常用不等式和先验估计证明该系统存在唯一的整体解,其次通过证明系统存在有界吸收集和半群的渐近光滑性得到整体吸引子的存在性.     

具有非线性热源项的耦合杆系统

主要以经典的算子半群理论为依据,研究了一类具有非线性热效应的耦合杆系统的长时间行为.首先在齐次边界条件和初始条件下,证明了系统解的存在唯一性;其次通过渐近先验估计,证明了系统有界吸收集的存在性;最后利用算子半群的分解技巧,得到了系统全局吸引子的存在性.     

吊桥方程指数吸引子的存在性

吊桥方程是工程数学中的一类重要数学模型.在非自治和自治两种情况下,吊桥方程紧整体吸引子的存在性已有许多结果.然而,这一问题指数吸引子的存在性还无人讨论.我们借助Eden等人提出的方法,证明了该问题指数吸引子的存在性.     

一类具有非线性kirchhoff-sine-Gordon广义方程的整体吸引子的存在性

主要目的是利用Galerkin逼近法和先验估计来证明一类具有非线性阻尼和外源项的耗散型sine-Gordon-kirchhoff方程的整体吸引子的存在性,首先通过先验估计证明系统存在唯一的整体解,再证明系统存在有界吸收集和算子半群光滑性质,最后得到系统存在整体吸引子.     

ZERO-DIMENSIONAL GLOBAL ATTRACTOR OF DAMPED SINE-GORDON EQUATION

1.IntroductionandMainResultsInthispaper,weconsiderthedampedsine-Gordonequation,withhomogeneousDirichletboundarycondition:whereu=u(x,t)ER,xEn,fiisaboundeddomaininRe(m=1,2,3)withsmoothboundaryoff,thedampingcoefficientor>0,thediffusingconstantd>0.Inthesequel,insteadofconsideringsystem(1.1),weinvestigatethefollowingsysteminHilbertspaceE=Ha(fi)xL'(fl):inwhichu(t)CHI(fl),v(t)6L'(fl)foranyt>0,A=--dA,G(u)=(--sine f),fEHa(~~),noEV.=Ha(~~),itoEH.=L'(fl).Let11'Onlayrwriteequatioll(l.2)asillwhi…     

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.     

The Dynamics of Sine-Gordon System with Dirichlet Boundary Condition

We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.     

LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

The three-dimensional nonlinear SchrSdinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.     

Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system

In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier-Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier-Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow.     

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.     

KGS格点系统的全局吸引子

考虑了对应于Klein-Gordon-Schrdinger方程的格点系统(KGS格点系统)的解的长时间行为．首先通过引入一个加权范数与采用解的“切尾”法,证明了全局吸引子的存在性．在此基础上,采用元素分解法与多面体的球覆盖性质, 得到了此吸引子的Kolmogorov δ-熵的上界的一个估计．最后,我们用有限维的常微分方程的全局吸引子逼近它．     

Exponential attractor of the 3D derivative Ginzburg-Landau equation

In this paper, we consider a derivative Ginzburg-Landau-type equation with periodic initial-value condition in three-dimensional spaces. Sufficient conditions for existence and uniqueness of a global solution are obtained by uniform a priori estimates of the solution. Furthermore, the existence of a global attractor and an exponential attractor with finite dimensions are proved.     

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．