弱解

Finally by constructing an auxiliary problem, using addition theorem and applying an iterative process based on results obtained for the linear problem, the existence and uniqueness of the weak generalized solution of the nonlinear problem is proved.

解决了线性问题后，本文构造了辅助问题，利用迭加原理，并基于线性问题的主要结论运用迭代过程，最终证明非线性问题存在唯一广义弱解。

Some nonexistence results for p-degenerate sub-elliptic first order evolution inequalities associated with the generalized Baouendi-Grushin vector fields are given. The method is an improvement of the admissible function method in Euclidean space. The proof hardly depends on the properties of the generalized Baouendi-Grushin vector fields.

通过改进欧氏的容许函数法，应用广义Baouendi-Grushin向量场的一些性质，选取特殊的容许函数，利用Hlder不等式和Young不等式，证明了由广义Baouendi-Grushin向量场构成的p-退化次椭圆一阶发展不等方程，在适当条件下非平凡弱解的不存在性。

Aragonite and calcite that is covered with an iron oxide stain can be cleaned with a weak solution of hydrochloric acid.

文石和方解石，就是盖了一个氧化铁染色可以清理一个弱解的盐酸。

Under some assumptions on the initial value, the asymptotic behavior of weak solutions for a fourth order degenerate parabolic equation with nonlinear relation is discussed.

在一些初值的假定下，讨论一个具有非线性关系的退化四阶抛物方程弱解的渐近行为。

The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.

具体安排如下：第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型，证明了该边值问题弱解的存在唯一性，在此基础上研究了自然电位测井电阻率识别问题：然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法，利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响，取得了满意的结果。

In this paper we will study the uniqueness of weak solutions of the first boundary value problem for a degenerate parabolic equation.

本文研究了一类具有退化性的抛物型偏微分方程的第一边值问题的弱解的唯一性。

The above result can be used to interpret the meaning of weak solution for some abstract boundary value problems.

上述结果可以用来解释抽象边值问题弱解的意义。

As rain falls, it dissolves carbon dioxide gas from the air and becomes a weak solution of carbonic acid.

下雨时，它会溶解的二氧化碳气体从空气中，成为弱解的碳酸。

In chapter two, we disscuss the nonexistence of global weak solution to elliptic equation with nonlocal sources where ai,j...

第二章，我们讨论了带有非局部源的椭圆方程全局弱解的不存在性-sum from i，j=1 to N ？

Tolksdorf [62] to prove the weak solutions of equation (2) are of C1,a if fand u are bounded with the help of some results in [40]. And by Morse iteration,we prove that the solutions are of C1,a even if f is of critical growth.

Tolksdor[62]的方法以及[40]中的一些定理证明了方程(1)弱解的C1，a的正则性；当f满足临界指数增长时，应用Morse迭代，我们首先证明了解的有界性，然后证明方程(1)的解也有C1，a的正则性。

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。