变分不等式

We first got the PML equations by making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Grding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experiments which show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Grding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Garding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

By using the compactness theorem of SBD space, Poincaréinequality onthe BD functions,we prove the existence for variational problems.

主要利用SBD函数空间的紧性定理，BD函数的Poincaré不等式等给出了变分问题的存在性。

To fill this gap, the enhanced Poincaré inequality was obtained by considering the additional conservation law of momentum and by rigorous estimate of integral inequality.

为解决这个差异，利用周期带域上的Eady模型的动量守衡的性质，通过变分方法和积分的精细估计，建立一个加强的Poincairé积分不等式，从而证明了Eady模型的线性稳定意味着非线性稳定。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

The first section introduces some basic concepts[9].The second section introduces Schmidt"s method of proving isoperimetric inequality [2].The third section introduces Hurwitz"s method [9].The fourth section takes from my tutors lecture notes.The method is due to REILLY [10].Finally,I make use of variational method to prove the circle among the curves of length L encloses the biggest area on the plane.

首先介绍了平面上的一些基本概念[9]，其次介绍了文献[2]中Schmidt证明等周不等式的方法，再次介绍了文献[9]中Hurwitz证明等周不等式的方法，然后介绍了导师吴发恩整理的文献[8]中REILLY的方法证明平面上的等周不等式[10]，最后我利用变分的方法证明了平面上等长的曲线围成的面积最大时为圆。

It is organized as follows:In Chapter 1, we introduce proximal point algorithms" framework and current research situation, optimization problems and variational inequalities" background and current research situation, and some basic concepts and lemmas, which are used in this dissertation.

本文具体安排如下：第一章简要介绍了邻近点算法的基本框架和研究现状，最优化问题和变分不等式问题的背景和研究现状，以及本文需要用到的一些基本概念和引理。

It is known that the VIP can be reformulated as an unconstrained minimization problem through the D-gap function.

我们知道，通过广义D-间隙函数，可以将变分不等式问题转化为一个无约束极小化问题。

And fixed point theory and the solution of variational inequalities on fuzzy mappings are also discussed.

并且也对模糊映射的不动点理论及变分不等式进行了一些讨论。

The first chapter is the theoretical foundation of the thesis.Some notations are introduced.

第一章 叙述论文中将要用到的有关变分不等式的一些常规记号和基础理论。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。