边界条件对非传播孤子运动的影响

用延拓法处理了非线性边值问题.指出第一类和第二类边界对非传播孤子的影响分别等效于某种势垒或势阱对经典弹性粒子的作用.研究了一对反相孤子在边界作用下的运动规律并得到与实验一致的结果. 关键词：     

带非线性边界条件的热传导方程的整体解与爆破问题

本文考虑下面的带有非线性边界条件的热传导方程的整体解的存在性及爆破问题，给出平衡解的分岐结果及整体解存在的充要条件．     

Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

粘滑混合边界条件下平面边界前的Stokes流动

对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.     

边界条件含特征参数的Sturm-Liouville问题的特征值比率

给出修正Prfer变换的几何意义以及相关性质,并利用上述性质讨论Sturm-Liouville问题-(py′)′+gy=λωy,x∈[0,1],参数边界条件为y(0)=0与((py′)(1))/(y(1))=aλ+b,得到了当a>0,q≥0的特征值比率上界,这把Ashbaugh等人的结果推广到边界条件含参数的情形.     

平面光波导器件时域有限差分束传输法分析中边界和初始条件的处理

从慢变包络（SVEA）时域光传输方程出发,对比了综合道格拉斯（GD）和传统的中心差分（CN）两种离散化格式,指出GD法比CN法精度有了很大提高.重点讨论了GD法的TD-BPM边界处理问题,给出了吸收边界和透明边界离散的显式和隐式表达式,分析并确定了交替方向隐式法（ADIM）的边界处理方式;同时,对激励源加入的连接边界进行了仔细讨论.结果表明对于隐式GD-TD-BPM法边界处理应采用隐式,中间激励更能反映光波导反射场的情况.     

Robin型离散Schwarz波形松弛算法的收敛性分析

Schwarz波形松弛(Schwarz waveform relaxation,SWR)是一种新型区域分解算法,是当今并行计算研究领域的焦点之一,但针对该算法的收敛性分析基本上都停留在时空连续层面.从实际计算角度看,分析离散SWR算法的收敛性更重要.本文考虑SWR研究领域中非常流行的Robin型人工边界条件,分析时空离散参数t和x、模型参数等因素对算法收敛速度的影响.Robin型人工边界条件中含有一个自由参数p,可以用来优化算法的收敛速度,但最优参数的选取却需要求解一个非常复杂的极小-极大问题.本文对该极小-极大问题进行深入分析,给出最优参数的计算方法.本文给出的数值实验结果表明所获最优参数具有以下优点:(1)相比连续情形下所获最优参数,利用离散情形下获得的参数可以进一步提高Robin型SWR算法在实际计算中的收敛速度,当固定t或x而令另一个趋于零时,利用离散情形下所获参数可以使算法的收敛速度具有鲁棒性(即收敛速度不随离散参数的减小而持续变慢).(2)相比连续情形下所获收敛速度估计,离散情形下获得的收敛速度估计可以更加准确地预测算法的实际收敛速度.     

Casimir Force on a Piston in Randall-Sundrum Models

The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall- Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force on the piston. We also discuss the Casimir force in the limit that one outer plate is moved to the remote place to show that the nature of the reduced force between the parallel plates left. In the Randall~undrum model involving two branes the two plates attract each other when they locate very closely, but the reduced Casimir force turns to be repulsive as the plates separation is not extremely tiny, which is against the experimental phenomena, meaning that the RSI model can not be acceptable. In the case of one brane model the shape of the reduced Casimir force is similar to that of the standard two-parallel-system in the four-dimensional fiat spacetimes while the sign of force remains negative.     

Generalized quantum mechanical two-Coulomb-center problem （Demkov problem）

We present a new exactly solvable quantum problem for which the Schro¨dinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two-Coulomb-center problem for the case of an imaginary intercenter parameter and complex conjugate charges are considered. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle rather than at separate points, there arise additional possibilities in the choice of boundary conditions. A detailed classification of the various types of boundary-value problems is given. The quasi-radial equation leads to a new type of boundary value problem which has never been considered before. Results of the numerical calculations, which allow conclusions to be drawn about the structure of the energy spectrum, are shown. Possible physical applications are discussed.     

带有等位面边界条件的抛物型方程

本文讨论一类与石油试井有密切联系的带有等位面边界条件的抛物型偏微分方程，对带有位面边界条件的热核函数进行了讨论，对方程解的梯度进行了估计，并给出了Ｈａｒｎａｃｋ型不等式，一类非线性抛物型方程与热方程的比较定理，以及在试井分析中应用的一个例子。