Ladyzhenskaya流体力学方程组的确定模与确定结点个数估计

论文给出了二维有界区域上Ladyzhenskaya流体力学方程组的确定模与确定结点的个数估计.结果表明若该方程组的任意两个弱解的前有限个傅立叶模有相同的渐近行为,则这两个解就具有相同的渐近行为;若该方程组的任意两个强解在有限个空间中的点上有相同的渐近行为,则这两个解几乎在整个空间上具有相同的渐近行为.     

具Neumann边界条件的Thin-Film方程解的爆破与熄灭

本文考虑具有非局部源的四阶Thin-Film方程的初边值问题.借助势井方法,得到了变号弱解整体存在和爆破的最佳条件.另外,研究了整体解的熄灭性质和非熄灭解的渐近行为.     

一类三阶梯度流方程弱解的稳定性[英文]

本文研究R~3上的一类三阶梯度流方程弱解的稳定性问题.我们分别证明弱解的一个全局稳定性结果和一个渐近稳定性结果.所得结果改进了已有文献中的一些关于三阶梯度流方程弱解的稳定性结果.     

一类非线性发展方程整体解的存在性、渐近性与解的爆破

研究一类非线性发展方程初边值问题整体弱解的存在性，渐近性和解的爆破问题，证明在关于非线性项的不同条件下，上述初边值问题分别在大初值和小初始能量的情况下存在整体弱解，并且讨论了弱解的渐近性。还证明：在相反的条件下，上述弱解在有限时刻爆破，并且给出了一个实例。     

修正Green-Sch能量的构造及应用

本文通过构造锥中修正的Green-Sch能量,不仅证明了锥中稳态Schrdinger方程弱解在无穷远点处除去一个例外集后的渐近行为,而且得到了锥中无穷远点处与Schrdinger算子相关的极细集和稀薄集新的性质.     

具有非局部边界的退化抛物方程组的爆破解

本文研究了具有非局部边界条件和非局部源的退化抛物方程组的弱解问题.利用基于比较原理的上下解的方法,在权函数和初始条件的假设下,获得了该方程组问题的爆破临界指标.此外,还获得了同时爆破解趋于爆破时间时的渐近行为,推广了已有的结果.     

Cahn-Hilliard-Brinkman系统的全局吸引子

研究了具有一般非线性条件的Cahn-Hilliard-Brinkman系统的弱解的适定性,分析了解的渐近性态,并通过渐近能量估计得到在H^s(Ω)(s=1,2,3,4)中全局吸引子的存在性.     

实轴上集序列的强渐近行为

首先基于点序列渐进分布的概念(分布函数是连续函数),提出实轴上集序列强渐近分布的概念(分布函数是绝对连续函数),是模1一致分布概念的推广.其次给出强渐近分布的Weyl型准则,改进Nakajima和Ohkubo的结果.最后利用强渐近分布的Weyl型准则研究一类实轴上迭代函数系统轨迹的强渐近行为.     

可压Navier-Stokes方程真空状态的动力学行为

本文主要考虑了一维可压Navier-Stokes方程真空状态的动力学行为.对于任意的熵弱解,如果初始状态不存在真空,我们证明了密度函数关于时间和空间变量是连续的且对于任意时间它是处处为正的.同时,我们还得到了含有间断连接的真空状态的整体熵弱解的存在性,结果显示其真空区域以代数速率被压缩,并在有限时间内消失.     

具有惯性项和阻尼项的Cahn-Hilliard方程的整体吸引子

本文研究具有惯性项和阻尼项的亚三次非线性Cahn-Hilliard方程的初边值问题.在非线性弱正则的条件下,我们建立弱解的适定性,而不考虑非线性项的一阶导数的下界条件.接着利用弱解的渐近紧和能量解的严格Lyapunov函数的存在性,证明在空间(H~2(?)∩H_0~1(?))×L~2(?)上存在整体吸引子.     

Optimal Solutions of Linear Periodic Control Systems with Convex Integrands

In this work we study the existence and asymptotic behavior of overtaking optimal trajectories for linear control systems with convex integrands. We extend the results obtained by Artstein and Leizarowitz for tracking periodic problems with quadratic integrands [2] and establish the existence and uniqueness of optimal trajectories on an infinite horizon. The asymptotic dynamics of finite time optimizers is examined. Accepted 31 January 1996     

Turnpike theorem for a class of set-valued mappings

In this work we study the asymptotic behavior of optimal trajectories for a class of superlinear mappings arising in economic dynamics. We establish the existence of an open everywhere dense subset F of the space of set-valued mappings such that each mapping fron F has the turnpike property.     

The asymptotic behavior of the strong solutions for a non-autonomous non-local PDE model with delay

In this paper, we study the asymptotic behavior of the strong solutions of a non-autonomous non-local PDE model with time delay. We present the existence and structure of the uniform attractor by constructing the skew product flow of the family of processes generated by the strong solutions. In order to obtain the existence of the uniform attractor, we prove the family of processes satisfies uniform condition (C) by using some special technique of phase space decomposition. Additionally, it is shown that all the bounded complete trajectories are globally asymptotic stable under some assumptions. As the application of our result, we obtain a globally asymptotic stable nontrivial strong periodic solution of a non-local PDE model.     

Global asymptotic stability analysis by the localization method of invariant compact sets

We study the asymptotic stability and the global asymptotic stability of equilibria of autonomous systems of differential equations. We prove necessary and sufficient conditions for the global asymptotic stability of an equilibrium in terms of invariant compact sets and positively invariant sets. To verify these conditions, we use some results of the localization method for invariant compact sets of autonomous systems. These results are related to finding sets that contain all invariant compact sets of the system (localizing sets) and to the behavior of trajectories of the system with respect to localizing sets. We consider an example of a system whose equilibrium belongs to the critical case.     

Hardy–Weinberg Theory for Tetraploidy with Mixed Mating

The dynamics of tetraploidy with mixed mating are studied, with fitness of inbreeders as a parameter. We determine the fixed points and the asymptotic behavior of the trajectories in the gametic and zygotic structures associated to this reproductive system. Our methods include elementary commutative algebra and algebraic geometry, and we make pervasive use of the computer program Macaulay2.     

Asymptotic Behavior of One-Parameter Semigroups and Rigidity of Holomorphic Generators

We study the asymptotic behavior of one-parameter continuous semigroups of holomorphic mappings. We present angular characteristics of their trajectories at their Denjoy–Wolff points, as well as at their regular repelling points (whenever they exist). This enables us to establish new rigidity properties of holomorphic generators via the asymptotic behavior of the semigroups they generate. Received: May 11, 2007. Accepted: July 22, 2007.     

半线性抛物型方程定义的光滑强单调流收敛于半渐近稳定的奇点

本文研究半线性抛物型方程定义的光滑强单调流的渐近性态，我们给出了具有有界轨线且不收敛于半渐近稳定奇点的点集在Ｘ￣α中是第一范畴的充要条件，我们还研究了全有序奇点弧的存在性和非平凡不变函数的存在性之间的等价关系。     

Topological Limit of Trajectories of Intervals of Simplest One-Dimensional Dynamical Systems

We consider dynamical systems generated by continuous maps of an interval into itself. We investigate the asymptotic behavior of the trajectories of subsets of the interval. In particular, we prove that if the -limit set of an arbitrary trajectory is a fixed point, then the topological limit of the trajectory of any subinterval exists.     

Asymptotic compactness of global trajectories generated by the Navier–Stokes–Poisson equations of a compressible fluid

In this paper, we consider the global behavior of weak solutions of Navier–Stokes–Poisson equations in time in a bounded domain–arbitrary forces. After proving the existence of bounded absorbing sets, we also obtain the conclusion on asymptotic compactness of global trajectories generated by the Navier–Stokes–Poisson equations of a compressible fluid. Supported by NSF(No:10531020) of China and the Program of 985 Innovation Engineering on Information in Xiamen University (2004–2007).