非线性扰动耦合Schrdinger系统激波的近似解法

研究了一类非线性扰动耦合Schrdinger系统.利用精确解与近似解相关联的特殊技巧,首先讨论了对应典型的耦合系统,利用投射法得到了精确的激波行波解.再利用近似方法得到了扰动耦合Schrdinger系统的行波渐近解.     

小展弦比波的Green-Naghdi渐进模型的行波解

本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解.     

一类非线性对偶系统的渐近解及其可解性条件

利用渐近理论,讨论了一类非线性对偶系统.在适当的条件下,得出了这一类非线性系统解的存在性条件及其渐近解.将此结果用于二自由度陀螺系统,较简捷地得到了该系统的具有小而有限振幅的渐近解.     

Liénard系统的比较定理

研究了Liénard方程的一类新的等价系统解的有界性与周期解的存在性.证明了几个比较定理,使传统Liénard方程等价系统解的有界性和周期解的存在性可用于判定新等价系统解的有界性与周期解的存在性.     

一类带记忆边界条件波动系统解的长时间性态

研究一类带记忆边界条件波动系统解的长时间性态.在初边值满足一定条件时,利用Faedo-Galerkin近似方法得到了系统解的存在唯一性.使用扰动能量方法,证明了系统解的一致衰减性.     

小展弦比波的Green-Naghdi渐进模型的行波解（英文）

本文研究了小展弦比波的Green-Naghdi渐进模型.利用平面自治系统的稳定性分析方法,在不同的参数条件下,讨论了它的行波系统的分岔并且给出了对应的相图,得到了光滑周期波解,广义扭波解,广义反扭波解,广义紧波解,周期尖波解,孤波解和孤立尖波解的精确表达式.进一步,通过数学软件Maple模拟了这些解.     

带有凹凸非线性项的Klein-Gordon-Maxwell系统解的存在性和多重性

研究一类Klein-Gordon-Maxwell系统解的存在性和多重性.当非线性项是凹凸非线性项时,利用变分方法获得了系统解的存在性和多重性结果,并完善了此系统解的存在性的已有结果.     

具有多重严重故障和非严重故障和修复功能的系统的可靠性分析

该文研究一个具有多重严重故障和非严重故障和修复功能的系统的可靠性问题. 在泛函分析理论的框架下,将系统方程组写成一个 Banach 空间中的抽象初值问题,利用算子半群方法,研究了该系统的适定性、稳态解的存在性以及稳定性.表明: 在系统模型的假定下,所研究的系统是适定的,存在非负动态解和稳态解, 特别在范数意义下动态解收敛到稳态解.从而由系统稳态解得到的系统指标是可靠的.     

具有饱和与竞争项的捕食系统的全局分歧及稳定性

利用比较原理,分歧理论,特征值线性扰动理论,主要研究了一类具有饱和与竞争反应项的捕食-食饵系统在Dirichlet边界条件下的平衡态分歧解.首先给出了一个先验估计和局部分歧解存在的充分条件.然后对局部分歧解进行了全局延拓,得到了该系统平衡态的全局分歧解及其走向.最后讨论了局部分歧解的稳定性.     

具有热储备的可修复平行系统在由常规错误引起失效下的渐进稳定性

讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用Banach空间的Volttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是mild解.但在t＞0时系统古典解存在唯一,所以此时mild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性.     

Dynamic analysis of a turbidostat model with the feedback control

In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution.     

Inverse problems of reconstructing parameters of the Navier-Stokes system

An inverse problem of reconstructing parameters not known a priori of the dynamical system described by the boundary-value problem for the Navier-Stokes system is considered. The reconstruction is based on one piece of admissible information or another about the motion of the dynamical system (solution of the corresponding boundary-value problem). In particular, one of the problems considered is the inverse problem consisting of reconstruction of the a priori unknown right-hand side of the Navier-Stokes system. The right-hand side characterizes the density of exterior mass forces acting on the system. This problem, as well as many other similar problems, is ill-posed. Two methods are proposed for its solution: the statistical method and the dynamical method. These methods use different initial information. In solving the problem by using the statistical method, initial information for the solution is the results of approximate measurement (in one sense or another) of the motion of the dynamical system on a given interval of time. Here, the reconstruction is performed after the corresponding interval of time. For solution of the problem by this method, the concepts and constructions of open-loop control theory are used. In solving the problem by using the dynamical method, initial information for its solution is the results of approximate (in one sense or another) measurements of the current states of the system, which are dynamically obtained by the observer. Here, the reconstruction is dynamically performed during the process. For solution of the problem by the dynamical method, the concepts and constructions of the dynamical regularization method based on positional control theory are used. Also, the author considers various modifications and regularizations of the methods for solution of problems proposed that are based on one piece of a priori information or another about the desired solution and solvability conditions of the problem. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear Dynamics, 2005.     

Periodic solution of a two-species competitive system with toxicant and birth pulse

In this paper, we study the existence of positive periodic solution of two-species competitive system with toxicant and birth pulse. A set of easily verifiable sufficient conditions are derived for the existence of at least one positive periodic solution of the above system by using the method of coincidence degree. Numerical simulations are also presented to illustrate the feasibility of our main results.     

On a method for solving a two-dimensional nonlinear integral equation of the second kind

In this article, the existence of at least one solution of a nonlinear integral equation of the second kind is proved. The degenerate method is used to obtain a nonlinear algebraic system, where the existence of at least one solution of this system is discussed. Finally, computational results with error estimates are obtained using Maple software.     

具有连续时滞和比率型功能反应的竞争系统的正周期解的存在性

本文利用重合度理论中的延拓定理讨论了具有连续时滞和比率型功能反应的非自治扩散竞争系统的正周期解的存在性,得到了正周期解存在的充分条件。     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

Chebyshev and L1 solutions of overdetermined systems of linear equations with bounded variables

Two algorithms are here presented. The first one is for obtaining a Chebyshev solution of an overdetermined system of linear equations subject to bounds on the elements of the solution vector. The second algorithm is for obtaining an L₁ solution of an overdetermined system of linear equations subject to the same constraints. Efficient solutions are obtained using linear programming techniques. Numerical results and comments are given.     

具有脉冲效应非自治捕食系统的研究

研究了具有脉冲效应的非自治捕食系统,该系统是两个具有互惠关系的食饵种群被一个捕食种群捕食.利用重合度理论证明系统正周期解的存在性.     

在常规错误下具有一个储备部件的冗余系统的稳定性分析

以在常规错误下具有一个储备部件的冗余系统为例,利用半群理论对系统算子的谱点分布进行分析,根据算子半群的稳定性原理,得出了该系统解的渐进稳定性的证明.