Navier-Stokes方程与Euler方程的稳定性比较

比较了Navier-Stokes 方程和Euler方程的稳定性;并以它们的典型初值问题为例,分析了Navier-Stokes方程和Euler方程稳定性不同的原因．     

圆锥曲线关于某点对称的曲线方程的应用

马志良(1947—),男,浙江普陀人,浙江普陀高级教师圆锥曲线ｃ:ｆ(ｘ,ｙ)=0(1)关于点Ｐ(ｘ0,ｙ0)对称的曲线ｃ′的方程为:ｆ(2ｘ0-ｘ,2ｙ0-ｙ)=0(2)利用方程(2)可求曲线ｃ在点Ｐ(ｘ0,ｙ0)处的切线方程和圆锥曲线ｃ以Ｐ(ｘ0,ｙ0)为中点的弦所在的直线方程.(1)-(2),得ｆ(ｘ,ｙ...     

Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.     

15个著名的不定方程问题

１５个著名的不定方程问题杨仕椿（四川西充县常林中学６３７２００）不定方程的研究，是数论研究中的热点与难点，它以其内容简洁易懂而方法艰深困难向人类的智慧提出挑战．除了著名的Ｆｅｒ－ｍａｔ大定理外，还有许多的其它不定方程问题，本文列举出１５个问题，逐一阐...     

INITIAL VALUE TECHNIQUES FOR THE HELMHOLTZ AND MAXWELL EQUATIONS

We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.     

一个扩散问题的自然边界元法与有限元法组合

本文讨论由Helmholtz方程描述的扩散问题的自然边界元法与有限元法的组合．取一个圆作为公共边界，用Fourier展开建立边界积分方程，将无界区域上的问题化为有界区域上的非局部边值问题．在变分方程中公共边界上的未知量只包含函数本身而不包含其法向导数，从而减少了未知数的数目，并且边界元剐度矩阵只有极少量不同的元素，有利于数值计算．这种组台方法优越于建立在直接边界元法基础上的组合方法．文中证明了变分解的唯一性，数值解的收敛性和误差估计．最后讨论了数值技术并给出一个算倒．     

几种广义非线性发展方程的新解

本文研究了构造了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解的问题.利用三种辅助方程及其新解,获得了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解.这些解由双曲余割函数、双曲正切函数、双曲正割函数、双曲余切函数和余割函数组成.     

含和不含外力项的KdV和MKdV方程的求解公式及各种类型的解

本文研究KdV和MKdV方程,其特点在于构造变系数非线性非齐次的偏微分方程及其求解公式,由于其系数是通用型的,故可通过变系数的适当选择,从中找到KdV和MKdV方程及其解,其实质是通过一个泛函把三阶的KdV和MKdV方程转变成4个任意函数的二阶方程来处理。本文获得了变系数KdV和MKdV方程及其孤立子解及含外力项的KdV和MKdV方程及其精确解。     

Vlasov方程的精确解

该文将等熵磁流体力学（ＭＨＤ）或等熵电磁流体力学（ＥＭＨＤ）的基本方程组以及（非相对论的或相对论的）Ｖｌａｓｏｖ方程，分别化为等熵流体力学（ＨＤ）表象，建立了上述三类等熵方程之间的对应关系．从而使非相对论Ｖｌａｓｏｖ方程的精确解（它与等熵ＭＨＤ方程的精确解相对应）和相对论Ｖｌａｓｏｖ方程的精确解（它与等熵ＥＭＨＤ方程的精确解相对应）都可以用（非相对论的和相对论的）等熵ＨＤ方程的精确解来表示．     

"同侧"同号,"异侧"异号及其拓广应用

1　命题的引入人教版全日制普通高中教科书 (试验本 )数学第二册 (上 )第 71页 ,对二元一次不等式表示的平面区域作了以下的阐述 :对直线Ａｘ+Ｂｙ+Ｃ =0同一侧的所有点 (ｘ,ｙ) ,实数Ａｘ+Ｂｙ+Ｃ的符号相同 ,所以只需在此直线的某一侧取一个特殊点 (ｘ0 ,ｙ0 ) ,从Ａｘ0 +Ｂｙ0 +Ｃ的正负即可判断Ａｘ+Ｂｙ +Ｃ>0表示直线哪一侧的平面区域 .特殊地 ,当ｃ≠ 0时 ,常把原点作为特殊点 .对此 ,笔者以下面命题来概括 :同侧同号 ,异侧异号 .2　命题的证明下面我们来证明该命题 .已知直线ｌ:Ａｘ +Ｂｙ+Ｃ=0 ,点Ｐ1(ｘ1,ｙ1)、Ｐ2 (ｘ2 ,ｙ2 ) ,…     

一类非线性时滞偏差分方程正解的不存在性

本文研究了一类非线性时滞偏差分方程正解的不存在性,得到了方程不存在 正解的判据。     

Global nonexistence of positive initial energy solution for coupled quasilinear system

In this paper, we consider global nonexistence of a solution for coupled quasilinear system with damping and source under Dirichlet boundary condition. We obtain a global nonexistence result of solution by using the perturbed energy method, where the initial energy is assumed to be positive. Copyright © 2017 John Wiley & Sons, Ltd.     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

Principal frequency and existence of solutions for quasilinear elliptic obstacle problems

In this paper, we are interested in the first eigenvalue of p-Laplacian and the relation between the first eigenvalue and the existence (or nonexistence) of nontrivial (positive) solution for quasilinear elliptic obstacle problems. Utilizing the fact that obstacle problem have consanguineous relations with corresponding equation, we get a simple approach to study the properties of solutions of obstacle problems, such as existence and nonexistence, regularity and stability, etc. In this paper we are mainly concerned with the existence and nonexistence.     

方程△g-aKg=0无正函数解的充分条件

Fischer-Colbrie和Schoen曾在1980年研究过复平面中单位圆盘当赋予某个完备度量时,方程Δg-aKg=0在其上无正函数解的充分条件,并将其结果应用到三维非负数量曲率流形中完备稳定的极小曲面上.这里Δ是Laplace算子,K为高斯曲率,a是常数,g是所讨论的单位圆盘上的函数.本文给出了此方程在该圆盘上无正函数解的一个更弱的充分条件.     

Existence and multiplicity of positive solutions to Schrödinger–Poisson type systems with critical nonlocal term

The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger–Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critical nonlocal case are completely different from the ones for the subcritical nonlocal system.     

Periodic solutions of neutral functional differential systems with two parameters

In this paper, we consider certain first-order neutral differential system with two parameters. Some existence results of one positive periodic solution and two positive periodic solutions and nonexistence of positive periodic solutions are obtained. Our approach is based on Krasnoselskii fixed point theorem in cones.     

Positive radially symmetric solution of the Dirichlet problem for a nonlinear elliptic system with <Emphasis Type="Italic">p</Emphasis>-Laplacian

Sufficient conditions for the existence and uniqueness of a positive radially symmetric solution of the Dirichlet problem for a nonlinear elliptic second-order system with p-Laplacian are obtained. In addition, it also proved that these conditions guarantee the nonexistence of a global positive radially symmetric solution.     

四阶奇异边值问题正解的多重性与无解性

应用不动点指数理论和上下解的方法,研究了一类非线性四阶微分方程组奇异边值问题,给出了其正解存在性与无解性定理.     

一类非线性四阶边值问题正解的存在性

利用锥拉伸和锥压缩不动点定理和上下解的方法,建立了一类四阶微分方程组奇异边值问题正解存在性与不存在性定理,推广了文[2],[3]的问题,进一步完善了文[2],[3]的相关结果.