弱解

In part III by using capacity theory and extension theorem of Lip-schitz functions we first discuss the uniqueness of weak solution ofnonhomogeneous quasilinear elliptic equations〓in space〓,which is bigger then〓.

第三部分首先用容量理论、Lipschitz函数延拓定理讨论了一类非齐次拟线性椭圆型方程〓在比〓更大的空间〓中弱解的唯一性。

For the non-homogeneous multi-dimensional scalar conservation laws, there is no existence theorem of global weak solution.

关于高维单守恒律方程的研究，对于非齐次的情形，至今还没有得到全局弱解的存在性定理。

Af ter applying this result to the conservative gas dy2 namic systems ,the semi2discrete finite difference approximation and the discrete ent ropy couple [Ut , F0j + G1j ] is searched.

关于双曲型守恒方程组ut + f x = 0 ，若存在标量熵对满足熵不等式Ut + Fx ≤0 ，则原方程存在弱解。

As a by-product, the global existence of weak solutions tothe multidimensional drift-diffusion model is obtained.

作为副产品，我们获得了高维漂移扩散模型弱解的整体存在性。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中，简要介绍了变分法的产生、发展过程，在第二章中我们介绍了有关变分法的一些基本知识，包括Sobolev空间，—△算子，弱解，极小化序列方法和一些极小极大定理，在第三章中我们介绍了非线性项有界或满足次线性条件，以及它满足推广的Ahmad-Lazer-Paul条件时，二阶Hamiltonian系统和半线性椭圆问题的研究历程，最后在第四章中我们证明了本论文的主要定理，并把它应用到第三章的问题中，使得前面的几种共振的情形都可以统一到这个抽象的结果中。

In chapter 4,we introduce the basic properties for pluripotential theory and results about the existence of weak solutions. Then we prove the existence of weak solution in some special domain which is not strictly pseudoconvex.

第四章我们先介绍多重位势理论的一些基本知识，然后介绍复Monge-Ampere方程在严格拟凸域上的已有的两个重要结论，之后讨论一类特殊的非严格拟凸域上复Monge-Ampere方程弱解的存在性。

In this paper, a finite element method for linear scalar conservation laws is analyzed.

研究了一维线性标量守恒律初边值问题的弱解，分析了有限元方法的收敛性。

The existence and uniqueness of Verhulst's partial differential equations on the population mathematical models were proved under an assumed condition by Schauder's fixed-point theorem and Gronwall's lemma.

讨论了在一定的假设条件下，Verhulst型人口模型弱解的存在性、唯一性和渐近性。

In Chapter 4,we prove the existence of global weak solutions to the compressible NSP equations with density-dependent viscosity coefficients when the initial data are large and spherically symmetric by constructing suitable aproximate solutions.

在第四章里，对于粘性系数依赖于密度的等熵可压缩NSP方程，在R~3中包含球心的球状区域内，我们得到了大始值的，球对称弱解的整体存在性。

Firstly, by use of the successive approximation method and a series of classical estimates, the local existence and uniqueness of weak solution are proved.

利用逐次逼近方法和一系列经典的估计，证明了弱解的局部存在性和惟一性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。