THE CLASSICAL SOLUTIONS TO A CAUCHY PROBLEM OF PARABOLIC TYPE COUPLED WITH OPERATORS

We consider the equation ut=Tf[B(x,t,Du,Φu)D^2u]+F(x,t,u,Du,Φu,Ψu) where Φand Ψ are vector-valued mappings.We obtain the existence anduniqueness of classical solution to the equation for a ε-periodic initial data.The problem is naturally arisen from image denoising.     

具有“on-off”过程的变分资料同化

为了验证伴随方法的有效性,利用一个含有"on-off"振荡的概念模式,研究了含物理参数化不连续性的变分资料同化中,代价函数关于初值梯度的存在性及伴随方法的可行性.结果表明:在解析情形中,尽管控制方程中出现"on-off" 振荡,代价函数关于初值的梯度除个别情形外总是存在的,且可由伴随模式的反向积分来表示.     

基于单位分解法的无网格数值流形方法

在数值流形方法和单位分解法的基础上，提出了无网格数值流形方法. 无网格数值流形 方法在分析时采用了双重覆盖系统，即数学覆盖和物理覆盖. 数学覆盖提供的节点形成求解 域的有限覆盖和单位分解函数；而物理覆盖描述问题的几何区域及其域内不连续性. 与原有 的数值流形方法相比，无网格数值流形方法的数学覆盖形状更加灵活，可以用一系列节点的 影响域来建立数学覆盖和单位分解函数，具有无网格方法的特性，从而摆脱了传统的数值流 形方法中网格所带来的困难. 与无网格方法相比，由于采用了有限覆盖技术，试函数的构造 不受域内不连续的影响，克服了原有的无网格方法在处理不连续问题时所遇到的困难. 详细推导了无网格数值流形方法的试函数和求解方程，最后给出了算例，验证了该方法的正 确性.     

一种类耗散系统的特征动力学行为

研究发现，在分段连续的保守系统中可能产生一种被称为“不连续性导致的不可逆性”，这种不可逆性可以导致一种“类耗散性”。它的表现之一是在原保守系统的混沌轨道中出现一个由不可逆性决定的“逃逸孔洞”，因之混沌迭代变为“类瞬态”，缓慢地从孔洞逃逸向某个规则运动的椭圆岛，在此数值地确定了逃逸的标度律。     

视像分解计算的讨论

本文从视像整体部分相互依存和对比反差不连续变化出发，给出了视觉图像的一种形式描述，并在此理论基础上，讨论了视像分解问题，得出任意可解析视像分解的一般性方法，其计算复杂性仅为Ｏ（ｎ）级。     

SENSITIVITY OF DARCY’S LAWTO DISCONTINUITIES

The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise constant coefficient K of the partial differential equation satisfied by the pressure u and it leads to the computation of the derivative of u with respect to changes in position of discontinuity surface of K.The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory. An application to a simple inverse problem is also given.     

负载特性激发的非线性项的不连续性跳跃

为了探索非线性系统的跳跃现象,研究了一个由代数方程描述的简单非线性系统。该系统中的非线性项在一定的参数组合及某些激励下会发生自异变行为。用负载线图解法分析了非线性元件自异变行为的产生原因、非线性项工作点轨迹与约束方程之间出现连续不相容现象。对不同的负载电阻,实验和计算机仿真结果表明,有跳跃滞的和完整的非线性特性曲线。负载电阻较小时,非线性项的特性曲线有些部分是不能观察到的,无法测量到单射的特性曲线,只能观察到有跳跃滞的不连续曲线。     

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.     

Double plate system with a discontinuity in the elastic bonding layer

The double plate system with a discontinuity in the elastic bonding layer of Winker type is studied in this paper. When the discontinuity is small, it can be taken as an interface crack between the bi-materials or two bodies (plates or beams). By comparison between the number of multifrequencies of analytical solutions of the double plate system free transversal vibrations for the case when the system is with and without discontinuity in elastic layer we obtain a theory for experimental vibration method for identification of the presence of an interface crack in the double plate system. The analytical analysis of free transversal vibrations of an elastically connected double plate systems with discontinuity in the elastic layer of Winkler type is presented. The analytical solutions of the coupled partial differential equations for dynamical free and forced vibration processes are obtained by using method of Bernoulli’s particular integral and Lagrange’s method of variation constants. It is shown that one mode vibration corresponds an infinite or finite multi-frequency regime for free and forced vibrations induced by initial conditions and one-frequency or corresponding number of multi-frequency regime depending on external excitations. It is shown for every shape of vibrations. The analytical solutions show that the discontinuity affects the appearance of multi-frequency regime of time function corresponding to one eigen amplitude function of one mode, and also that time functions of different vibration basic modes are coupled. From final expression we can separate the new generalized eigen amplitude functions with corresponding time eigen functions of one frequency and multi-frequency regime of vibrations. The English text was polished by Keren Wang.