Euler-Possion 半导体模型的大时间行为

本文研究了Euler-Poisson半导体模型弱熵解的大时间行为, 得到了一致有界的弱熵解随着时间t指数衰减到稳态解. 本文的结果不需要假定解是``小"的, 也不需要假定解的正则性.     

房地产开发活动均衡分析与过度开发行为控制

在把房地产投资开发项目看作为一种具有弱再生性经济资源的基点上,对房地产投资开发活动进行了均衡分析,讨论了房地产开发活动中的最优平衡解及其相互之间的制约关系,分析了税收和配额价格等经济参数对最优平衡解的影响,给出了抑制房地产过度投资开发行为的控制模型与方法,并得出了相应的政策启示.这些研究结果,可以推广应用于其他各种可再生资源的投资开发与管理当中去,有着广泛的应用前景.     

一类半线性椭圆型方程爆炸解的存在性与渐近行为

设Ω是Ｒ＾Ｎ（Ｎ≥２）中的Ｃ＾２有界区域,对非线性项带有适当的梯度与无界系数ｋ（ｘ）,首先应用非线性变换将爆炸解问题,转化成等价的带奇异项的Ｄｉｒｉｃｈｌｅｔ问题,应用极大值原理得到爆炸解问题的最小爆炸速度。随后,应用摄动方法,结合上下解方法与椭圆型方程的估计理论得到了爆炸解的存在性。     

Kawahara-BO方程Cauchy问题的局部可解性

研究Kawahara-BO方程在低正则Sobolev空间Hr上的局部适定性和极限行为.证明了:当r>-7/5时,对任意的初始值uo ∈Hr,Kawahara-BO方程的Cauchy问题存在唯一的解u∈C([0,T],Hr)∩Xr,s;当BO项系数λ趋向于O时,Kawahara-BO方程的解收敛到Kawahara方程的解.     

二阶半线性奇摄动边值问题解的渐近行为

该文研究非法向双曲条件下的二阶半线性奇摄动边值问题解的渐近行为.利用边界层函数法,构造了区间端点处的代数型边界层,获得了问题的一致有效渐近解;利用微分不等式理论,证明了解的存在性以及渐近解与精确解之间的误差估计.通过一个典型的算例,验证了该文的理论结果.     

外部区域上的一类半线性伪抛物型方程

本文主要考虑在外区域上的一类半线性伪抛物型方程的解的长时间行为.本文得到的临界指标揭示了边界上的非齐次条件将对解的长时间行为产生本质影响.     

二阶耗散动力系统的降维对解长期行为的误差估计

基于非线性动力学理论,对一类高维二阶耗散自治动力系统的降维及其对解的长期行为的影响进行了理论分析．该分析将方程的解投影到控制方程的线性算子的特征向量所张成的完备空间中,并在相空间中引入一距离的概念,方便地解决了缩减后系统与原始系统解之间的误差或距离的描述．基于此距离定义,首先,分析了由于高阶模态的截取对解的长期行为的影响,并推导出了相应的误差估计,该估计表明由于降维对系统长期行为的影响不仅与系统的高阶子空间中的固有频率和阻尼比乘积的最小值有关,并且与高阶子空间中的某一最大固有频率有关．然后,将一般的模态截取视为对原系统的解的一个扰动,对一些文献中由于降维程度的不同而造成解的拓扑性质发生变化的现象进行了定性的解释．     

半导体材料科学中的能量输运模型

这是一篇关于半导体材料科学中能量输运模型的综述性章。该在这两个方面讨论了具有绝缘边值的两种典型能量输运模型的初边值问题，一方面得到了一种强解的存在性，另一方面得到了光滑解全局存在性和大时间行为。     

食物受限人口模型中非线性延迟微分方程数值解的振动性

本文讨论食物受限人口模型中的一个非线性延迟微分方程数值解的振动性.通过应用两种θ-方法,即线性θ-方法和单腿θ-方法,构造指数θ-方法,得到数值解振动的条件,进一步考虑非振动解的渐近行为,最后给出两个数值算例.     

含时滞的线性偏泛函微分方程解的渐近行为

本文对一类含有时滞的抛物偏泛函微分方程解的渐近行为进行了讨论。分别就两种不同的边界条件，采用Ｌｉａｐｕｎｏｖ泛函及Ｌ—ｐ—估计，获得了其解全局稳定、振动的若干简洁充分条件     

Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation

We apply the method of homotopy analysis to the Zakharov system with dissipation in order to obtain analytical solutions, treating the auxiliary linear operator as a time evolution operator. Evolving the approximate solutions in time, we construct approximate solutions which depend on the convergence control parameters. In the situation where solutions are strongly coupled, there will be multiple convergence control parameters. In such cases, we will pick the convergence control parameters to minimize a sum of squared residual errors. We explain the error minimization process in detail, and then demonstrate the method explicitly on several examples of the Zakharov system held subject to specific initial data. With this, we are able to efficiently obtain approximate analytical solutions to the Zakharov system of minimal residual error using approximations with relatively few terms.     

On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis

This paper deals with large time behaviors of solutions to a Keller–Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in details.     

Large time behavior of Euler-Poisson system for semiconductor

In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions converges to the stationary solutions exponentially in time.No smallness and regularity conditions are assumed.     

时滞速度反馈对强迫自持系统动力学行为的影响

研究强迫自持振动系统因时滞反馈产生的主共振解及其分岔．通过对强迫非自治系统的时滞反馈控制,得到所要研究的数学模型．讨论对应的线性化系统使平凡平衡态失稳出现周期解的稳定性临界条件．特别关注主共振及分岔．结果表明,稳定的主共振解随着时滞的变化周期性地出现在系统中．同时,也给出了不稳定的主共振关于时滞变化的区域,在理论方面给出了系统出现概周期运动的时滞区域．数据模拟证实了理论结果．     

Relaxation approximation of the Euler equations

The aim of this paper is to show how solutions to the one-dimensional compressible Euler equations can be approximated by solutions to an enlarged hyperbolic system with a strong relaxation term. The enlarged hyperbolic system is linearly degenerate and is therefore suitable to build an efficient approximate Riemann solver. From a theoretical point of view, the convergence of solutions to the enlarged system towards solutions to the Euler equations is proved for local in time smooth solutions. We also show that arbitrarily large shock waves for the Euler equations admit smooth shock profiles for the enlarged relaxation system. In the end, we illustrate these results of convergence by proposing a numerical procedure to solve the enlarged hyperbolic system. We test it on various cases.     

Existence of periodic solutions to a system with functional response on time scales

This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.     

The necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional differential equations

In this paper, using Fourier series, we study the problem of the existence of periodic solutions of a type of periodic neutral differential difference system. Some necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional equation system are obtained, and at the same time, we present a method with formula shows how to find the periodic solutions.     

Eine parabolische Gleichung mit vergänglichen Lösungen

We give an example of a parabolic system having solutions which blow up in a finite time interval. This system is contrasted with a very similar system whose solutions go on for all time.     

Structure of Solutions of Discrete Time Optimal Control Problems in the Regions Close to the Endpoints

We study the structure of approximate solutions of an autonomous nonconcave discrete-time optimal control system with a compact metric space of states. This control system is described by a bounded upper semicontinuous objective function which determines an optimality criterion. In our recent research we showed that approximate solutions are determined mainly by the objective function, and are essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time interval. In the present paper we study the structure of approximate solutions in regions close to the endpoints of the time intervals.     

时间测度上具有时滞基于半比率的捕食者-食饵扩散系统的周期解

在时间测度上研究一类具有时滞和基于半比率且有功能性反应的两种群捕食者-食饵扩散系统,利用Mawhin重合度理论建立了这类系统的周期解存在的一个充分性判据.从而使这一类系统的连续与离散情形即相应的微分方程和差分方程的周期解存在性问题得到了统一研究.