二维空间中广义Davey-Stewartson系统整体解存在的最佳条件

根据基态的特征 ,首先在二维空间中导出了广义Davey Stewartson系统解爆破和整体存在的最佳条件 ;其次得到了整体解存在的一个最佳充分条件 ;最后证明了当初值为多小时 ,该系统的整体解存在 .     

解算子与右端数据均有扰动的半正定算子方程的动态系统方法

本文研究了求解算子与右端数据均有扰动的第一类半正定算子方程的动态系统方法.证明了相应的动态系统Cauchy问题的整体解存在且收敛于原算子方程的解.此外,给出了解Cauchy问题的迭代方法并证明了方法的收敛性.     

解算子与右端数据均有扰动的半正定算子方程的动态系统方法

本文研究了求解算子与右端数据均有扰动的第一类半正定算子方程的动态系统方法．证明了相应的动态系统Cauchy问题的整体解存在且收敛于原算子方程的解．此外,给出了解Cauchy问题的迭代方法并证明了方法的收敛性．     

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.     

一类具有非线性阻尼的梁系统的整体吸引子

利用经典的算子半群理论,研究了一类具有非线性阻尼和非线性外力项的梁方程的初边值问题,证明了系统解的存在唯一性,然后引入一个算子半群;利用经典的算子半群分解方法,证明了系统存在整体吸引子.     

广义双色散热耦合方程组的初边值问题

研究了一类广义双色散热耦合方程组的初边值问题在齐次边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性;其次通过证明系统的衰减性和渐近紧性,得到了系统存在全局吸引子;最后证明了该系统的全局吸引子存在有限分形维数.     

具结构阻尼的耦合梁方程组在非线性边界条件下的吸引子

研究了具有转动惯量和结构阻尼的耦合梁方程组在非线性边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性,其次证明了系统存在有界吸收集和半群的渐近光滑性,最后得到了全局吸引子的存在.     

阻尼对带逆平方势的非线性Schrodinger方程整体解的影响

本文研究一类带阻尼和逆平方势的非线性Schrodinger方程. 旨在关心阻尼对系统整体解的影响. 对于系统的次临界情形, 通过引入一个特殊的变换和运用反证法, 我们证明了阻尼并不影响系统的整体解：系统的解对于任意初值都整体存在. 对于系统的临界和超临界情形, 我们分析了阻尼对系统的影响,运用变分法构建了一类适用于任何阻尼强度的系统整体解存在的准则.     

种群扩散系数互异系统解的一致有界性

采用积分估计的方法证明了弱耦合反应扩散系统整体解的存在性和一致有界性,该系统是扩散系数互异的食物链模型,并通过举例进一步说明该方法的普适性.     

非均匀介质中双稳型反应对流扩散方程的整体解

本文研究了非均匀介质中双稳型反应对流扩散方程的整体解(t∈R).通过利用连接常数稳定态和不稳定态的曲面行波解,证明了整体解的存在性,该整体解表现为两列曲面行波解从无穷柱体两端相向传播、相互碰撞、并最终在有限时间内合并.进一步,在一定条件下,证明了方程的非平凡整体解是唯一的,并利用上下解方法证明了所得到的唯一整体解是Liapunov稳定的.     

具弱耗散项的非线性Hartree方程

该文讨论了一类在量子理论中有着较多应用的具耗散项的非线性Hartree方程。分别从耗散系数和初值两个方面讨论了解的整体存在性条件。一方面,利用Strichartz估计,得到仅依赖于耗散系数的整体存在性条件。另一方面,也得到了仅依赖于初值大小的整体存在性条件。而且,还得到了一个整体解存在的小初值准则。     

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.     

The global existence of solutions for two classes of chemotaxis models

This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases.     

Global error bound for convex inclusion problems

The existence of global error bound for convex inclusion problems is discussed in this paper, including pointwise global error bound and uniform global error bound. The existence of uniform global error bound has been carefully studied in Burke and Tseng (SIAM J. Optim. 6(2), 265–282, 1996) which unifies and extends many existing results. Our results on the uniform global error bound (see Theorem 3.2) generalize Theorem 9 in Burke and Tseng (1996) by weakening the constraint qualification and by widening the varying range of the parameter. As an application, the existence of global error bound for convex multifunctions is also discussed.     

Heat flow of harmonic maps from noncompact manifolds

The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.     

Global well-posedness of coupled parabolic systems

The initial boundary value problem of a class of reaction-diffusion systems(coupled parabolic systems)with nonlinear coupled source terms is considered in order to classify the initial data for the global existence,finite time blowup and long time decay of the solution.The whole study is conducted by considering three cases according to initial energy:the low initial energy case,critical initial energy case and high initial energy case.For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence,long time decay and finite time blowup are given to show a sharp-like condition.In addition,for the high initial energy case the possibility of both global existence and finite time blowup is proved first,and then some sufficient initial conditions of finite time blowup and global existence are obtained,respectively.     

一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

饱和Activator-Inhibitor模型柯西问题的整体解

本文首先证明了饱和Activator－Inhibitor模型柯西问题整体解的存在性，其次考虑到Activator对源密度的反馈效应，又证明了具有反馈的上述模型整体解的存在性．     

Global attractor for heat convection problem in a micropolar fluid

The article is devoted to describe asymptotics in the heat convection problem for a micropolar fluid in two dimensions. We show the existence and the uniqueness of global in time solutions and then prove the existence of a global attractor for considered model. Next, the Hausdorff dimension of the global attractor is estimated. Copyright © 2006 John Wiley & Sons, Ltd.     

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris‘ result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.