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.     

一致渐近稳定和周期解、概周期解的存在性

本文建立了系统解一致稳定、解一致渐近稳定和某种Liapunov函数存在的充要条件,并且得到:满足Lipschitz条件而且解一致渐近稳定的概周期系统有唯一的概周期解,周期系统有唯一的周期解。     

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.     

一类具有优化调整状态的供应链系统的稳定性分析

主要研究一类具有优化调整状态的供应链系统解的适定性问题,利用C_0-半群理论和谱分析的方法,得到了此系统存在惟一的时间依赖解,并且当时间趋于无穷时,该时间依赖解收敛于其稳态解,而其稳态解恰好是系统算子的0本征值对应的本征向量.     

退化时滞中立型微分系统解的存在唯一性及指数估计

本文主要讨论退化时滞中立型微分系统解的存在唯一性及指数估计问题.通过定义正则矩阵对讨论退化时滞中立型微分系统解的存在唯一性.再定义基解矩阵以及Laplace变换,给出该系统的通解表达式,最后利用通解表达式和Gronwall-Bellman积分不等式给出该系统解的指数估计及解的精确指数界限.     

种群生理结构模型解的性质

考虑具有生长率的种群生理结构动力学模型,讨论了系统解的渐近性质,当系统具有多平衡解时,指出各平衡解的稳定性。     

含奇异线的广义KdV方程的行波解

研究了一个广义KdV方程的行波解,在行波变换下,该方程转化成含奇异线的平面系统,通过平衡点分析定性地得到不同参数条件下系统解的特性.特别的,由于相平面上的奇异线的存在,系统具有一些特殊结构的解,例如compactons、kink-compactons、anti-kink-compactons,给出了这些解的积分表达式,并且由椭圆函数积分求出了精确解.     

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.     

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.     

一类带修理工休假可修系统解的存在唯一性及正则性分析

考虑一类修理工可多重延误休假的n部件串联可修复系统解的存在唯一性及正则性问题.通过将系统模型方程转化为一组算子积分方程,利用不动点理论讨论该系统局部解的存在唯一性问题,再由一致先验估计和连续延拓讨论系统整体解的存在唯一性问题,继而分析解的正则性问题.为解决复杂可修复系统解的存在唯一性及正则性提供了可行性方法,并且方法同样适用于排队论系统和其他类似系统.     

常规故障和定期维修的冗余系统的指数稳定性

利用C_0-半群理论证明了具有常规故障和定期维修的冗余系统非负解的存在唯一性,并研究了相应算子的谱特征,通过分析本质谱界经过紧扰动后的变化,得到系统动态解以指数形式收敛于稳态解.     

修理工可单重休假的带有一个冷贮备部件的Gaver并联系统的时间依赖解的渐进行为

研究修理工可单重休假的带有一个冷贮备部件的Gaver并联系统的时间依赖解.运用C₀-半群理论与算子理论研究该模型相应算子的谱的特征,获得了该系统的时间依赖解强收敛于该系统的稳态解.     

具有一种故障类型的二相关单元冗余系统的指数稳定性

利用C_0-半群理论证明了具有一种故障类型的二相关单元冗余系统非负解的存在惟一性,并研究了相应算子的谱特征,通过分析本质谱界经过紧扰动后的变化,得到了系统动态解以指数形式收敛于稳态解.最后,给出几个数值模拟的例子用来说明本文的意义所在.     

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.     

两不同部件并联可修系统解的稳定性

用强连续算子半群理论证明了两不同部件并联可修系统解的存在唯一性和非负性，并通过研究相应算子的谱特征得到了该系统的稳定性。     

A spectral domain decomposition approach for the generalized Burger’s–Fisher equation

In this study, we use the spectral collocation method using Chebyshev polynomials for spatial derivatives and fourth order Runge–Kutta method for time integration to solve the generalized Burger’s–Fisher equation (B–F). Firstly, theory of application of Chebyshev spectral collocation method (CSCM) and domain decomposition on the generalized Burger’s–Fisher equation is presented. This method yields a system of ordinary differential algebraic equations (DAEs). Secondly, we use fourth order Runge–Kutta formula for the numerical integration of the system of DAEs. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.     

A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning

In this study, we use the spectral collocation method using Chebyshev polynomials for spatial derivatives and fourth order Runge–Kutta method for time integration to solve the generalized Burger’s–Huxley equation (GBHE). To reduce round-off error in spectral collocation (pseudospectral) method we use preconditioning. Firstly, theory of application of Chebyshev spectral collocation method with preconditioning (CSCMP) and domain decomposition on the generalized Burger’s–Huxley equation presented. This method yields a system of ordinary differential algebric equations (DAEs). Secondly, we use fourth order Runge–Kutta formula for the numerical integration of the system of DAEs. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.     

一个供应链系统可靠性模型时间依赖解的渐近行为

本文研究一个供应链系统可靠性模型的时间依赖解.利用C0-半群理论研究该模型相应算子的谱的特征,获得了该系统模型时间依赖解的渐近行为,推广了文献[8]中的结果.     

A Study of the Direct Spectral Transform for the Defocusing Davey-Stewartson II Equation the Semiclassical Limit

The defocusing Davey-Stewartson II equation has been shown in numerical experiments to exhibit behavior in the semiclassical limit that qualitatively resembles that of its one-dimensional reduction, the defocusing nonlinear Schrödinger equation, namely the generation from smooth initial data of regular rapid oscillations occupying domains of space-time that become well-defined in the limit. As a first step to studying this problem analytically using the inverse scattering transform, we consider the direct spectral transform for the defocusing Davey-Stewartson II equation for smooth initial data in the semiclassical limit. The direct spectral transform involves a singularly perturbed elliptic Dirac system in two dimensions. We introduce a WKB-type method for this problem, proving that it makes sense formally for sufficiently large values of the spectral parameter k by controlling the solution of an associated nonlinear eikonal problem, and we give numerical evidence that the method is accurate for such k in the semiclassical limit. Producing this evidence requires both the numerical solution of the singularly perturbed Dirac system and the numerical solution of the eikonal problem. The former is carried out using a method previously developed by two of the authors, and we give in this paper a new method for the numerical solution of the eikonal problem valid for sufficiently large k. For a particular potential we are able to solve the eikonal problem in closed form for all k, a calculation that yields some insight into the failure of the WKB method for smaller values of k. Informed by numerical calculations of the direct spectral transform, we then begin a study of the singularly perturbed Dirac system for values of k so small that there is no global solution of the eikonal problem. We provide a rigorous semiclassical analysis of the solution for real radial potentials at k=0, which yields an asymptotic formula for the reflection coefficient at k=0 and suggests an annular structure for the solution that may be exploited when k ≠ 0 is small. The numerics also suggest that for some potentials the reflection coefficient converges pointwise as ɛ↓ 0 to a limiting function that is supported in the domain of k-values on which the eikonal problem does not have a global solution. It is expected that singularities of the eikonal function play a role similar to that of turning points in the one-dimensional theory. © 2019 Wiley Periodicals, Inc.     

A semigroup approach to the Gnedenko system with single vacation of a repairman

We investigate the Gnedenko system with one repairman who can take vacations. Our main focus is on the time asymptotic behaviour of the system. Using C ₀-semigroup theory for linear operators we first prove the well-posedness of the system and the existence of a unique positive dynamic solution given an initial value. Then by analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we show that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution.