Kuramoto-Sivashinsky方程解的定性分析

研究Kuramoto-Sivashinsky方程的两种初边值问题,运用Galerkin方法给出一系列先验估计结果,得到广义解和古典解的存在唯一性、正则性及某些条件下的渐近性质。     

Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the state of the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits originate in various discontinuity-induced bifurcations. We also show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.     

Numerical Solution of the Eigenvalue Problem for Discontinuous Linear Ordinary Differential Equations

The eigenvalue problem for linear ordinary differential equationswith discontinuous terms is considered. It is shown that onecan effectively use Atkinson's product integration techniquestogether with a Green's function to solve the problem numerically.     

Solution techniques for the Large Set Covering Problem

Given a finite set E and a family F={E₁,…,E_m} of subsets of E such that F covers E, the famous unicost set covering problem (USCP) is to determine the smallest possible subset of F that also covers E. We study in this paper a variant, called the Large Set Covering Problem (LSCP), which differs from the USCP in that E and the subsets E_i are not given in extension because they are very large sets that are possibly infinite. We propose three exact algorithms for solving the LSCP. Two of them determine minimal covers, while the third one produces minimum covers. Heuristic versions of these algorithms are also proposed and analysed. We then give several procedures for the computation of a lower bound on the minimum size of a cover. We finally present algorithms for finding the largest possible subset of F that does not cover E. We also show that a particular case of the LSCP is to determine irreducible infeasible sets in inconsistent constraint satisfaction problems. All concepts presented in the paper are illustrated on the k-colouring problem which is formulated as a constraint satisfaction problem.     

二维浅水波方程的间断周期解和间断孤立波解讨论

本文讨论地球流体运动浅水波模式中间断周期解与间断孤立波解.在系统的非平衡点即奇点附近考虑轨线性质时,我们发现只要引入广义解的概念(分片光滑连续解),就会产生间断周期解并得到了间断周期解的条件.当系统在退化的过程中,发现系统此时会产生间断的孤立波解,与此同时其它物理量也产生了间断.这里我们发现,一般认为在超高速情况下解会产生间断,然而在非超高速时也会产生间断现象.本文讨论了上述一系列问题得到了间断解的解析解表达式,并把这一事实与飑线的实例进行比较,得到了不少类似之处.     

间断动力学系统多媒体仿真

研究了常微分方程组右函数间断的问题,讨论了间断处理算法的基本思想与关键因素,构造了合适工程计算的速度、精度、稳定性相协调的实用间断处理算法.遵循建模-仿真-表现一体化的多媒体仿真方法,将仿真实验所产生的信息和数据转变成为被感受的场景、图示和过程,直观展现了间断系统内在运动规律和外在表现形式.仿真实验的结果表明该方法是有效可行的.     

Some Qualitative Properties for the Total Variation Flow

We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations.     

物元可拓集集合性质研究

在可拓集合概念基础上,提出了向量可拓集和区间可拓集概念,研究了物元可拓集合的交、并、求补等集合运算及其性质.     

无穷区间上一类不连续非线性积分方程的唯一解

在一般Banach空间中研究了一类无穷区间上不连续非线性积分方程的唯一解．在非常弱的条件下证明了非线性积分方程的唯一解可以由迭代序列的一致极限得到，并给出了逼近解的迭代序列的误差估计式，然后应用到无穷区间一阶微分方程的终值问题，本质改进（将紧型条件删去）并推广了一些结果．     

On the Solution Existence of Generalized Quasivariational Inequalities with Discontinuous Multifunctions

We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E ^*, a multifunction and a multifunction Γ:X→2 ^X , find a point such that , . We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous. The authors express their sincere gratitude to the referees for helpful suggestions and comments. This research was partially supported by a grant from the National Science Council of Taiwan, ROC. B.T. Kien was on leave from National University of Civil Engineering, Hanoi, Vietnam.     

弱向量变分不等式解集的连通性

研究拓扑向量空间到连续线性映射空间映射的弱向量变分不等式和与之相关 的纯量型变分不等式解集的关系, 引入弱和强一致连续概念,利用纯量型变分不等式 解集所表征的集值映射的特性给出弱向量变分不等式解集连通的一个充分条件。     

The Essential Component of the Solution Set for Vector Equilibrium Problems

In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector equilibrium problem satisfying some conditions. Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China.     

含间断项的非线性积分、微分方程极解的存在性

在不涉及紧型条件和耗散型条件的情形下，证明了Ｂａｎａｃｈ空间中含间断项的非线性积分、微分方程极解的存在性，推广了文［１］、［２］和［３］中的结果．     

有效解集的自动生成方法

本根据多目标规划有效解集的特性,应用神经网络的逼近和分类功能,建立了多目标规划有效解集的自动生成方法,证明了有关定理,给出了应用示例。     

一类不连续系统关于闭不变集的有限时间稳定性研究

主要研究右端不连续系统在Filippov解意义下关于闭不变集(未必是紧集)的有限时间稳定问题.当Liapunov函数是Lipschitz连续的正则函数情况下,给出了相关的Liapunov稳定性定理.     

Toeplitz Operators on the Fock Space with Presymbols Discontinuous on a Thick Set

Toeplitz operators with discontinuous presymbols on the Fock space are studied. These presymbols can have two limit values at the points of some subset in ?ⁿ, generally speaking of nonzero measure. Nevertheless the Toeplitz operator algebra still admits a commutative symbolic calculus.