具有结构阻尼的热弹性梁耦合系统的整体解

考虑热效应对弹性梁的影响,研究了一类具有结构阻尼的热弹性梁耦合系统的整体动力行为,采用Galerkin方法证明了该系统整体弱解的存在唯一性.     

周期摄动守恒系统的数值解

讨论了周期摄动非线性守恒系统。利用Hadamard定理证明了在适当的条件下连续问题解的存在唯一性。并在均匀网格上对方程作了离散化,给出了相应的离散问题具有唯一解的结果。最后讨论了数值解的精度及有关算法。     

Exact Controllability of a Semilinear Thermoelastic System with Control Solely in Thermal Equation

A result concerning the exact controllability of a semilinear thermoelastic system, in which the control term occurs solely in the thermal equation, is derived under the influence of rotational inertia and Lipschitz nonlinearity, subject to the clamped/Dirichlet boundary conditions. In the proof, we make use of the result given by Avalos (Differential and Integral Equations, 2000; 13(4–6):613–630), which states that the corresponding linear system is exact controllable.     

Necessary and Sufficient Conditions of Existence and Uniqueness of Limit Cycles for a Polynomial System

In this paper, the following polynomial system is discussed:And the necessary and sufficient conditions of existence and uniqueness of limit cyclesare obtained.     

一类非线性耦合双曲型方程组的研究

研究了一类非线性耦合双曲型方程组初边值问题,讨论了初边值条件以及非线性项中指数满足的条件,利用Galerkin方法和紧致性的结果,以及椭圆型方程解的正则性定理,经过严格的推导证明了该问题解的存在唯一性的若干结果.     

具阻尼的非线性耦合方程组的能量衰减估计

应用一个新的积分不等式,得到了具阻尼的非线性耦合方程组的衰减估计,以及精确的估计常数.     

Existence and Uniqueness of Smooth Solution for a Four-waves Coupled System

In this paper, we consider a four-waves coupled system which describes the interaction between particles. Based on the uniform bound and strong convergence property in lower order norm, local existence and uniqueness of smooth solution is established by a limiting argument. Moreover, we show the solution exists globally in two dimensional case under certain condition on the size for $L^2$ norm of the initial data.     

一类非稳态热耦合方程组解的存在性和正则性

In this paper,a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied.Existence of a weak solution is first established through a result of Meyers' theorem and Schander fixed point theorem,where the coupled functionsσ(s),k(s) are assumed to be bounded in the C(IR×(0,T)).Ifσ(s),k(s) are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution.The regularity of the solution in dimension n≤2 is then analyzed...     

种间作用的二维非线性动力系统模型及其数值模拟试验研究

系统探讨了种间制约作用的二维非线性动力系统的机理与过程,从生物力学角度扩展了Lotka-Volterra模型,建立了包含种间作用与反作用的二维非线性自治、非自治动力系统新模型,分析了该动力系统平衡点的稳定性、周期解的存在性与稳定性,并对其动力学过程进行了数值模拟试验研究.结果表明两生物种群间作用效率的大小、作用系数与反作用系数变化的同向与异向性和作用力时变等对动力系统稳定性都有一定影响,种间作用效率变大或变小,以及作用系数与反作用系数的异向变化都导致动力系统的不稳定,致使两种生物难以生存,而相互作用力时变则对系统的稳定起促进作用.     

Quantitative properties on the steady states to a Schrödinger–Poisson–Slater System

In this paper, we obtain the existence, uniqueness and asymptotic behavior of steady states to a class of Schrödinger-Poisson-Slater System.     

The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology space...     

一类人为错误可修复系统的指数稳定性分析

随着科学技术的发展,特别是电子产品和网络的运用,系统的可靠性分析变得日益重要.在Dhillon B S和Yang N F(1993)中通过增补变量的方法建立了这类系统的数学模型并进行研究.在此基础上进一步讨论系统解的渐进稳定性和指数稳定性,证明了系统算子在Bnacha空间中可以转化为C_0半群,0是系统算子的简单本征值,而且是系统在虚轴上唯一的谱点.此外本文还分析了在系统扰动前后系统算子解的基本谱,结果显示系统的动态解以指数稳定性趋向于系统的稳态解,通过maple作图发现系统稳定解有时候不一定趋向于系统的实际解,这对实际运用有重要的指导意义.     

非线性多层渗流系统的数值方法及其应用

对多层非线性渗流系统提出适合并行计算的迎风分数步差分格式，利用变分形式、能量方法、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧，得到收敛性的最佳阶的误差估计．该方法已成功的应用到油资源渗流力学运移聚集数值模拟的生产实际中．     

Global Existence and Nonexistence for a Strongly Coupled Parabolic System with Nonlinear Boundary Conditions

This paper deals with the strongly coupled parabolic system ut = v^m△u, vt = u^n△v, （x, t） ∈Ω × （0,T） subject to nonlinear boundary conditions 偏du/偏dη = u^αv^p, 偏du/偏dη= u^qv^β, （x, t） ∈ 偏dΩ × （0, T）, where Ω 包含 RN is a bounded domain, m, n are positive constants and α,β, p, q are nonnegative constants. Global existence and nonexistence of the positive solution of the above problem are studied and a new criterion is established. It is proved that the positive solution of the above problem exists globally if and only if α 〈 1,β 〈 1 and （m ＋p）（n ＋ q） ≤ （1 - α）（1 -β）.     

非线性Schrodinger方程的一种数值模拟方法

该文通过对非线性Schr\"{o}dinger方程增加耗散项,提出了一种新的三层线性差分格式.证明了该格式满足连续方程所具有的两个守恒量及收敛性和稳定性.通过数值例子与已知格式进行比较,结果表明该格式计算简单且具有较高精度.     

Mathematical Modeling of Near-Field Optics

Consider a time-harmonic electromagnetic plane wave incident on a periodic (grating) structure. An inhomogeneous (subwavelength) object is placed inside the periodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has many physical and biological applications. This work is devoted to modeling and analysis of a near-field optics problem. An integral representation approach is presented to solve the problem. It is shown particularly that the perturbation due to the object decays exponentially along the periodic direction of the structure, provided that no surface waves occur. Based on the approach, a general solution method is discussed and the well-posedness of the model problems are established.     

一类平面微分系统极限环的存在唯一性

研究一类平面微分系统的极限环,利用Hopf分支理论得到了该系统极限环存在性的若干充分条件,利用Л.А.Чеpкас和Л..Иилевьтч的唯一性定理得到了极限环唯一性与稳定性的若干充分条件.     

偶数阶非线性微分方程的周期解

This paper deals with even order nonlinear differential equations. Applying the Schauder fixed point theorem and the Schwartz inequality technique, we give a criterion to ensure the existence and uniqueness of periodic solutions. This criterion is a complement of the well known Lazer type results.