Brusselator方程解的存在性和稳定性

本文研究了一种Brusselator方程的。用不变区域证明了解的全局存在性，并通过构造上下解给出了非常数定态解渐进稳定的条件。最后推出吸引域。     

复域双周期Riccati方程解空间极限集的复杂性

研究了一个复域上双周期系数的Riccati方程,证明了其解空间可分成三个不相交的子空间,其中一个子空间为闭集,所有周期解的全解析延拓的闭包包含在这个子空间内并形成一个完备子集。该子集在解的延拓变换群下是最小不变闭集,可能具有分形结构,而任一周期解的全解析延拓均在此子集内稠密。     

随机哈密尔顿系统的周期变差解和近不变环面解

本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.     

关于Poisson积分的一个注记

<正> 在一类混合型偏微分方程的研究中,华罗庚提出了一个新的观点:把它看成为单位圆(推广便是典型域)的 Laplace-Beltrami 算子,即和空间运动群下不变 Riemann 度量对偶的不变算子.这个方程在区域的内部是椭圆的,在区域的外部是双曲的,而在区域的边界上是退化的.熟知在椭圆区域有 Dirichlet 问题,其解可用 Poisson 积分表出.华罗     

伴有边界条件摄动的向量二阶半线性奇摄动问题解的估计

本文利用微分不等式的不变域理论,研究当ε→0~ 时向量二阶半线性边值问题εy″=g(x,y,ε)=y,(0,ε),A(ε),y(1,ε)=B(ε)解的存在和渐近性质,得到了包括边界层在内的任意阶近似的一致有效的渐近解。     

一类非对称可递域的调和函数

<正> 把单复变函数论中调和函数的概念推广到多复变函数论中去,有好几种方法.1959年华罗庚与陆启铿把调和函数定义为下列微分方程的解 u:(?)其中 T~(-1)(z,(?))是所考虑的域的度量方阵 T(z,(?))之逆方阵,z=(z_1,z_2,…,z_n).这种定义方法的优点是使调和函数在域的解析同胚下不变.他们对这种调和函数解决了四类典型域的 Dirichlet 问题,得到了很好的结果.但是,他们的方法只用到典型域的可递     

KD-拉回吸引的非自治动力系统拉回吸引子的存在性及其应用

利用拉回吸引子的存在性理论,证明了具有KD-拉回吸引的非自治动力系统拉回吸引子的存在性,拉回吸引子是单点集,是不变的.对无解域上的非自治反映扩散方程,证明了拉回指数吸引子的存在性,是方程唯一拉回指数吸引的稳定解.     

水轮发电机定子系统磁固耦合双重共振

以双壳系统模型为水轮发电机定子系统的物理模型,建立了三相对称稳态运行状态下定子系统的磁固耦合振动方程.分析了定子系统磁固耦合的双重共振,指出其响应具有跳跃现象,在某些参数域上有多解共存现象.     

等维Cartan-Hartogs域双全纯映射的特征（英文）

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域ΩB(μ)不是球,则它上面存在一函数X使得它在ΩBm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维CartanmHartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域ΩB(μ)不是球,ΩBm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

非均匀介质中波动方程的部分不变解

讨论了来自于非均匀介质中波动方程的部分不变解的存在性，证明了在波速满足适当的条件下部分不变解是存在的，并得到了部分不变解。     

STABILITY OF BOUNDARY LAYER TO AN OUTFLOW PROBLEM FOR A COMPRESSIBLE NON-NEWTONIAN FLUID IN THE HALF SPACE

This paper investigates the large-time behavior of solutions to an outflow problem for a compressible non-Newtonian fluid in a half space. The main concern is to analyze the phenomena that happens when the compressible non-Newtonian fluid blows out through the boundary. Based on the existence of the stationary solution, it is proved that there exists a boundary layer(i.e., the stationary solution) to the outflow problem and the boundary layer is nonlinearly stable under small initial perturbation.     

MULTIPLE BOUNDARY LAYER PHENOMENA OF THE SOLUTION OF NONLINEAR HIGHER ORDER ELLIPTIC EQUATIONS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

1IntroductionInmanyproblemsofmechanicsandphysics,therefrequentlyappeartheellipticequationswiththederivativetermofthehigherordercontainingsmallparameters.Inengineering,thehigherorderellipticequationswithbothboundaryperturbationandoperatorperturbationoccurintheproblemsofcircularorellipticcoluxnnarshell(suchasthehullofasubmarineorthecolumnarshellroofetc.)withstiffeningribinthecirculnferentialdirection.Insuchcasesjthestudyofweldingstresscausedbyexternalpressureorself-weightduetoabnormalweldingposi…     

Heat and mass transfer investigation of rotating hydrocarbons droplet which behaves as a hard sphere

The steady state boundary layer equations around rotating pure hydrocarbon droplet are solved numerically. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method where Thomas algorithm solves the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hexane droplet concluded. The thickness of the boundary layer is unknown for this model and therefore, it is determined. Further, this work proposes correlations of Nusselt and Sherwood numbers for monocomponent hydrocarbon droplets in evaporation. These correlations consider the rotation phenomena and further, the variation of the thermophysical and transport properties in the vapour phase.     

关于奇摄动拟线性系统

本文目的在于对非线性两点边值问题(1.1)证明其解存在的充分条件。并利用这一结果研究拟线性弱耦合奇摄动系统(DP)q的边界层现象。     

Long-wave dispersion phenomena in a layer subject to elastically restrained boundary conditions

A generalisation of the usual free and fixed-face boundary conditions for an elastic layer is considered. Specifically, this is in the context of a linear isotropic elastic layer and involves an investigation into long-wave motion. Elastically restrained boundary conditions are introduced, with both a numerical investigation and a multi-parameter asymptotic analysis employed to elucidate dispersion phenomena in a layer subject to such boundary conditions. The characteristics of mode transformations associated with the change from traction-free to fixed-face boundary conditions are described, focusing particularly on the fundamental modes which are known to not occur in the case of fixed faces. All possible asymptotic regimes are grouped into six classes, with the corresponding expansions of frequency in respect of wave number derived.     

Internal and boundary calculations of thin elastic bodies

A method for the separate construction of the main stress-strain state (the internal calculation) and the boundary corrections (the boundary calculations) are discussed in the case of a linear static problem in the theory of shells and plates. It is assumed that the internal calculation is carried out using an iterative process based on the Kirchhoff-Love theory. The boundary calculation involves the construction of antiplane and plane boundary layers, that is, in the initial approximation they reduce to the solution of antiplane and plane problems in the theory of elasticity.

Investigation of the asymptotic behaviour of the boundary corrections shows that near a weakly clamped edge only the correction from the antiplane boundary layer is important and that near a fairly rigidly clamped edge only the correction from the plane boundary layer is important.

The advisability of the use of the shear theory of the bending of plates for investigating boundary elastic phenomena is discussed from the point of view of the results obtained. It is shown that, close to the free edge, its use is justified and is adequate for the method described in the paper both with regard to the numerical results and with regard to the nature of the mathematical apparatus. As a method for investigating boundary elastic phenomena, shear theories lose their meaning close to a fairly rigidly clamped edge since they only enable one to construct the minor part of the correction asymptotically.     

奇摄动高阶椭圆型方程解的多重边界层现象

研究了一类奇摄动2m阶椭圆型方程解的多重边层现象．利用比较定理得到解的一致有效的渐近展开式．     

一类具有局部弱稳定退化解的奇摄动Robin问题

研究一类一般的二阶非线性方程的奇摄动Robin问题的边界层现象.在退化解是局部弱稳定的主要假设下,利用界定函数法和微分不等式理论证明了呈边界层性态的解的存在性,并给出解的渐近估计.     

一类双参数三阶半线性方程边值问题的奇摄动

研究一类双参数三阶半线性方程边值问题的奇摄动，讨论了摄动解随两参数的不同量级所呈现的不同性态的边界层现象，并给出了解的一致有效的渐近展开式．