一维边值问题

Firstly, we discuss the boundary value problem of one dimensional biharmonic equation in an interval and its variational problem,multiresolution analysis in the Sobolev space , then solve it with wavelet-Galerkin methods.

首先本文讨论了一维双调和方程边值问题及其相应的变分问题，定义Sobolev空间的多分辨分析，用小波–伽辽金方法进行数值求解，两组基下得到的系数矩阵为七对角阵和块状对角阵。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

In this article, a class of nonlinear elliptic boundary value problems with singular coefficient in one-dimensional domain was considered.first of all existence and uniqueness of the weak solution of the variational problem correspondin

本文考虑如下一维四阶非线性奇异边值问题 Lu=D~2p(xD~2u-Dp(xDu+pu=fx，u(x x∈I≡(0，1)u(0)=u′(0)=0 u(1)=u′(1)=0的有限元方法。给出相应问题广义解的存在唯一性和先验估计，并通过与解的E-范数投影相比较得到Galerkin逼近的L_2和最大

At last, we are concerned with the global existence and asymptotic behavior of smooth solution to the initial boundary value problem for the bipolar hydrodynamic model with the Neumann and Dirichlet boundary condition in the one-dimensional case, respectively. The difficulties from the coupled action between electrons and holes are carefully dealt with.

另外，本文也深入研究一维空间双极半导体流体动力学模型初边值问题光滑解的整体存在性及其衰减性，分别讨论了两类在实际应用中重要的边值条件，克服了由于电子和空穴之间的耦合作用所带来的困难。

Within this context, four specific areas are addressed:(1) By means of finite integration technique, a new kind of the first order partial difference equation is derived from the original disperse transmission line equation of the uniform waveguide's. As it is the kind of one dimension Dirichlet's boundary problem, it is convenient for us to solve this equation from the leapfrog scheme. Because computation is carried out in one dimension, both high calculation efficiency and precision have been obtained in this method. Meanwhile, this method provide us a different selection to simulate the transient response of waveguide with non-simplical, for examples cylinder and elliptic waveguide, and avoid solving the second order equation, or using finite difference time domain to simulate a three dimension problem, sometimes the latter precision is not satisfied with the need, or low efficiency.

在这一研究内容下，主要研究四个方面的问题：(1)在完成金属波导传输线方程时域形式的基础之上，应用有限积分技术，把波导特征模式的色散传输线方程，化简为一组新的一阶偏微分方程组，该边值问题属一维Dirichlet边值问题，从而便于用蛙跳格式求解，由于是在一维中计算，该方法具有很高计算效率和精度，从而避免了以往为得到金属波导中特征模的时域响应特性，须要求解二阶方程，或用时域有限差分方法求解三维问题的方法，对于后者来说，计算有时是不准确的，或是很耗时的例如计算诸如圆波导、椭圆波导等其它复杂形状的波导。

In the first part we consider the convergence and stability of finite difference scheme for Landau-Lifshitz equation in one dimensions space and 2d radial symmetric Landau-Lifshitz equation.

在第一部分，我们研究一维Landau-Lifshitz方程非齐次边值问题和二维柱对称Landau-Lifshitz方程Neumann边值问题的有限差分格式。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

The GKS stability theorem for one-dimensional model of hyperbolic initial and boundary value problem, Trefethen's explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of MTF is pointed out based on his explanation and extension, namely, coupling effect of outgoing harmonic wave along one direction and node motion in the other directions can reverse the energy propagation in multi-dimensional discrete grids.

本文概述了—维双曲型偏微分方程组初边值问题数值稳定性的GKS定理及Trefethen基于群速度概念对这一定理的解释和推广；并应用Trefethen的解释和推广指出了MTF在数值实现中可能出现的另一种高频失稳机制，即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。

In this paper,based on an improved orthogonal expansion in an clement , using the new idea of Ref.[3] ,a new error expression of n-degree Hermite finite element approximation to one-dimensional 4-degrec 2-point bounded problem and 2-degree ordinary differential problem, and then optimal order superconvergence for their first derivatives is obtained.

本文针对在改进的单元正交性估计的基础上，利用文[3]提出的新想法，得到一维四阶两点边值问题和二阶常微初值问题的n次赫米特有限元u_h∈C~1的新误差估计式，以及导数误差的最佳阶超收敛，并且两者有相同的超收敛结果。

Then, in second part, we consider the existence and uniqueness of global regular solution for one-dimensional and 2-D radial symmetric Landau-Lifshitz equation.

第二部分我们研究一维Landau-Lifshitz方程齐次Neumann边值问题和二维柱对称Landau-Lifshitz方程Neumann边值问题解的正则性。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。