查询词典 boundary condition

It is proved by using the function approximation theory and martrix theory that for a degenerate elliptic equation of the first class, if the third boundary value condition is satisfied at its nondegenerate boundary and the given derivative values are satisfied at its degenerate boundary, then its solution is existent and unique.

摘 要 运用逼近理论及矩阵理论证明：如果一类退化椭圆型方程在非退化边界上满足第三边界条件，在退化边界上满足给定微商值，那么它的解是存在且唯一的。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

The no-penetration boundary condition is satisfied by placing a vortex sheet along the boundary, which strength must be adapted to cancel the slip velocity on the boundary induced by all the other flow components.

本论文以Leonard之面积扩散涡漩法及Huang之涡泡分裂融合修正法为基础，开发一满足无滑移、无穿透边界条件之数值模拟工具。

The full space calculation model, which suits for the asymmetric structure sometimes even including air below the surface of medium, can enable simulative result to approach real one. The FDTD algorithm based on the mixed ABCs is proper to calculate the transmission line where the electromagnetic wave is transmitted in order to send electromagnetic energy along central conductor. The calculation efficiency will be raised if the PML absorbing boundary condition is set on both planes of transmitting direction and so is the MUR two-order absorbing boundary condition in the other planes.

全空间计算模型是适合所有的不对称结构的待研究体的，而且包括了介质下面的空气部分，使仿真更加的接近实验真实情况；基于MUR-PML混合吸收边界条件的时域有限差分法非常适合计算传输线这种结构，因为传输线是传送电磁波的，电磁能量主要是沿着中心导带行进，因此在两个传输端面上设置PML完全匹配层吸收边界条件，在其他面上设置MUR二阶吸收边界条件，会大大提高计算效率，而且计算结果与XFDTD仿真软件计算结果相比较，基本趋于一致。

In the third part, we discuss a simple class of Sturm-Liouville problems with Dirichlet boundary condition in the first boundary condition and an affine function in the second one.

第三部分我们讨论了一类参数边界条件的Sturm-Liouville问题，其第一边界条件为Dirichlet条件，第二个边界条件为特征值参数的线性函数。

This technique is used for the axisymmetric magneticstatic problems and the result is good. In the second example of the forth chapter, the error of the third–order Asymptotic Boundary Condition is lower than that of the second-order Asympototic Boundary Condition.

第五章针对这一问题，进一步对渐近边界条件进行了推导，分析了一些特殊电荷和电流分布情况下，电位、标量磁位和矢量磁位的多极矩展开式中各极矩项的性质。

Based on the perfectly matched layer absorbing boundary condition, a new form of PML absorbing boundary condition in cylindrical coordinate suitable for optical fiber is derived.

在已有的完全匹配层吸收边界条件的基础上推导了圆柱坐标系下适用于光纤计算的PML吸收边界条件。

Based on the variable separation method, the governing equations for the film thickness problem have been solved. A reasonable consistent condition of the momentum equations has been found and solved. Based on the methods ofmathematical physics, series expansion solution of the velocity filed in the film has been derived. A boundary condition at the boundary of the spray area was given and the velocity slip phenomenon has been considered.

基于电子器件喷雾冷却技术的研究现状和研究热点，本文对喷雾在热源表面形成的冲击液膜流动及厚度模型、基于CHF(Critical Heat Flux，临界热流密度)准则的倾斜喷射喷嘴轨迹、喷嘴距热源换热最优时的高度、倾斜喷射实验以及针对动态喷射的电磁驱动器件的吸合问题等方面进行了研究：针对圆锥形轴对称喷雾冷却系统，在对喷雾区域进行划分的基础上，引入滑流边界条件，在提出圆锥状喷雾假设的基础上，建立了喷雾区域雾滴密度连续介质等效模型。

In this dissertation, the author discusses the numerical solution for the direct acoustic scattering problem with the Neumann boundary condition, and pays more attentions to discuss numerical recovering the shape of the obstacle region, which is the inverse problem of the direct acoustic scattering problem with the Dirichlet or impedance boundary condition.

本文重点研究了Neumann边界条价下的声波障碍散射正问题和Dirichlet、Impedance边界条件下的声波障碍散射区域反问题的数值计算方法，得到很好的理论结果和数值结果。

In this paper,regularization method is introduced. The author pays more attentions to investigate the numerical solution for the direct acoustic scattering problem with the Dirichlet boundary condition, and the numerical recovering the shape of the obstacle region which is the inverse problem of the direct acoustic scattering problem with the Dirichlet boundary condition.

本文主要引入正则化方法，研究了针对Dirichlet边界条件的声波障碍正散射问题和声波障碍散射反问题的数值计算方法，并得到了很好的数值结果。

"Bird Man's Diary, Butting on the Love Island", Changsha, China

2008年"鸟人日记，顶在爱情岛"，中国长沙

As long as they were in the service of a family of wizards, their magic would remain dormant.

只要他们一天为家庭服务，他们的法力就潜藏不动。