查询词典 cauchy kernel

On this newconcept, we succeed to prove the uniqueness of Cauchy Problem of the aboveequation by the methods of using the Hausdorff measure of the set of the discontinuous points of BV solution and Kruzkov technique etc.

基于此概念，通过对BV函数的间断点集合Hausdorff测度的仔细分析，以及利用Kruzkov技巧等我们证明了上述方程BV解的存在唯一性。

It is concluded that the inversion of unknown boundary data is more effective when the Cauchy data are given more precisely and are distributed on the whole boundary more diversely.

由数值的结论，我们认为只要柯西资料给定的越准确，并且在全边界上给定的越分散，则会有越好的结果。

Chapter 6, consider a coupled generalized KdV-Burgers equation. In section 6.2, we study the initial-boundary value problem in the semi-unbounded domain, the existence of global solutions and global attractors is proved by means of a uniform priori estimate for time. In section 6.3, the Cauchy problem by using the weighted space, the existence of the global attractors for a coupled generalized KdV-Burgers in an semi-unbounded domain is proved.

第六章，考虑了一类广义耦合的KdV-Burgers方程，在第二节中讨论了半无界区域上的初边值问题，证明了整体光滑解和整体吸引子的存在性；在第三节中讨论了Cauchy问题，利用加权函数和加权空间上的插值8不等式，证明了半无界区域上整体吸引子的存在性。

We discussed the coupled generalized BBM equations with pseudodifferential operator in Chapter three.In this chapter we get the global existence for the Cauchy problem by Banach-fixed point theorem ,a priori estimates and Sobolev embedding theorem.

第三章讨论了具拟微分算子的广义BBM方程组，通过Banach不动点定理、解的先验估计和Sobolev嵌入定理得到了解的整体存在性。

Some closedforms of formulae are also obtained for the evaluation of the Cauchy prin-cipal integrals over quadratic boundary elements and linear internal cells of2-D problems.

通过采用以上各种技术成功地解决了三维弹塑性有限形变问题边界元法中最关键的数值积分的精度和效率问题。

In this thesis.Cauchy problem of evolution equation is discussed.

对于大多数形如上两式的方程，解不容易写出。

In course of the education reform of complex function theory ,the author uses the exterior differential tools shortly to prove well—known Cauchy theorem and formulas.

在复函数论的教学改革中，利用外微分工具简洁地证明了著名的柯西定理和公式。

Keywords nonlinear elastodynamic system, Cauchy problem, exterior problem,almost global existence, null condition.

非线性弹性动力学方程组； Cauchy问题；外问题；几乎整体存在性；零条件

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

In this paper it has been proven that for Cauchy problem of quasi-linear homogeneous partial differential equation its solution always has discontinuity , and the trace of discontinuity is just the envelope of characteristic lines.

本文证明对于拟线性齐次偏微分方程的Cauchy问题，其解总具有间断性，且发生间断的点的轨迹，恰巧就是特征线的包络，另外给出了一个特例，否定了这类解必定会出现多值性的定性论断，从而使构造广义解的理论面临困难。

The receding calculations and experiment analyses in this subject are built on the blood cast of pig tongue.

本研究课题的前期工作是采用猪舌血管铸型模拟人舌而进行的数值计算与实验分析。

"Each human infection constitutes an opportunity for genetic modification of the virus through reassortment, mutation, or both...."

&每一次人类的感染都暗藏着一次基因修改的机会，无论是通过病毒的整合、突变或者兼而有之。。。。&