APPROXIMATE CONTROLLABILITY OF THE STOKES EQUATIONS WITH BOUNDARY CONDITION ON THE PRESSURE

In this paper, some properties of three-dimensional Stokes equations with boundary condition of pressure on parts of boundary are studied. By use of these properties, approximate controllability by tangent boundary controls acting on a subboundary is studied. In addition, the controllability problem is considered when its controls act on a subdomain.     

A NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION WITH MOVING GRIDS FOR STOKES PROBLEM

This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.     

变边界热传导方程差分格式的收敛性

在许多工程技术领域中,常常提出求解变边界非线性热传导方程,例如,空间技术领域中的烧蚀传热问题.由于物体表面处于高温环境的影响,表面出现烧蚀状态,物体的厚度随时间的变化而递减.因为物体温度很高,物体的导热率、比热、密度强烈地依赖于物体的温度.因此,传导系数不仅是空间坐标的函数,而且也是物体温度的函数.     

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。     

由近场谱数据确定阻抗散射体的形状

本文考虑由点源波入射，在获取近场散射数据时具有阻抗边界的散射体的重构问题．区别于N．Grinberg利用Herglotz波函数和单层势的途径，我们利用混合互易关系，得到了远场和近场算子的关系，由该关系和奇异值分解，得到了算子的谱，从而将散射体特征化．数值实验表明，能得到良好的重构．     

含开边界二维Stokes问题的Galerkin边界元解法

本文推导了含有开边界的二维有限域上Stokes问题的边界积分方程, 得出基于单层位势的第一类间接边界积分方程.对与之等价的边界变分方程用Galerkin边界元求解以得出单层位势的向量密度. 对于含有开边界端点的边界单元,采用特别的插值函数, 以模拟其固有的奇异性.论文用若干数值算例模拟了含有开边界的有限区域上不可压缩粘性流体的绕流.      

ON MAXWELL EQUATIONS WITH THE TRANSPARENT BOUNDARY CONDITION

In this paper we show the well-posedness and stability of the Maxwell scattering problem with the transparent boundary condition. The proof depends on the well-posedness of the time-harmonic Maxwell scattering problem with complex wave numbers which is also established.     

GLOBAL SOLVABILITY OF NONLINEAR WAVE EQUATION WITH A VISCOELASTIC BOUNDARY CONDITION

The paper deals with the global solvability of nonlinear wave equation with a viscoelastic boundary condition. The problem is a mathematical mode for nonlinare one-dimensional motion of an elastic bar connected with a viscoelastic element at one end of the bar. Under some physically reasonable assumptions, the boundary condition is dissipative and the existence of global smooth solution of the problem is proved for small data.     

UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

This paper considers the inverse acoustic wave scattering by a bounded penetra-ble obstacle with a conductive boundary condition.We will show that the penetrabl...     

具非线性边界条件的奇异扩散方程

本文讨论具非线性第二边界条件的一端无界的奇异扩散方程的初边值间题,利用先验估计方法得到的主要结果是:存在唯一的整体光滑解,且解连续依赖于初值．