查询词典 weak solution

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。

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 3,we consider the Cauchy problem of transportation equation 〓Which is referred to as the simplification model of gas dynamics equations with constantpressure,and prove the existence and uniqueness of weak solution.

在第三章，我们考虑了运输方程〓，2的Cauchy问题，并且证明了广义解的存在性。最后，我们考虑下列二维Cauchy问题〓通过引进新的广义解定义，证明了解的存在唯一性。这个解可能含〓波。

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

O1 c compactness of the entropy equation; At last, coupling with Kinetic formulation, we can obtain the existence of a strong convergent sequence, then the limit function is just the entropy weak solution of the original systems.3. Existence of global entropy solutions to an inhomogeneous elastodynamics system.

o1 c紧性，最后结合Kinetic理论得到粘性解存在强收敛的子列，从而可得该极限函数即为原方程组的熵弱解。3、研究了一类非齐次弹性力学方程组整体熵解的存在性。

At the same time, the SEM study shows that gibbsite occurs on the sample surface. At 200 ℃, as dawsonite sandstone is being dissolved authigenic siderite forms. At 300℃, chlorite deposit on parts of the sample surface. The weak solution of dawsonite sandstone at 100℃ and the formation of siderite at 200℃ illuminate that CO2 being in carbonates in the strata can not be released when CO2 phase is adding to the system.

同时，各温度下样品表面均有一水软铝石放射状集合体沉淀。200℃时，随着片钠铝石的溶解有自生菱铁矿生成，300℃时样品局部有绿泥石沉淀。100℃下片钠铝石的微弱溶解及200℃下菱铁矿的形成表明，在地层条件下以碳酸盐矿物形式捕获的CO2，不会由于CO2的二次注入而重新释放。

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 ？

The existence of weak solution for quasilinear elliptic system in the whole space is studied.

讨论了在全空间上拟线性椭圆型方程组的非平凡解的存在性。

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。

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。