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...     

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．     

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。     

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.     

应用改进的简单方程法求非线性数学物理方程的精确解

应用改进的简单方程法求得Cahn-Allen方程和Jimbo-Miwa方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可以得到了孤立波解.当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,简单方程法对于研究非线性数学物理方程具有非常广泛的应用意义.     

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．     

Riccati方程解法的启迪

在一定条件下,Riccati方程可经函数的分式线性变换化为变量分离方程求解。     

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...     

Lindel(o)f的工作与Chaplygin的工作的互补性

运用Ｖａｋｏｎｏｍｉｃ模型导出Ｌｉｎｄｅｌｏｆ方程,表明Ｌｉｎｄｅｌｏｆ的工作与Ｖａｋｏｎｏｍｉｃ模型相吻合,运用Ｃｈｅｔａｃｖ模型导出Ｃｈａｐｌｙｇｉｎ６方程,表明Ｃｈａｐｌｙｇｉｎ的工作与Ｃｈｅｔａｅｖ模型相吻合,在此基础上,通过改进Ｃｈａｐｌｙｇｉｎ方程的Ｌｉｎｄｅｌｏｆ方程的表示形式,实现了从Ｌｉｎｄｅｌｏｆ方程向Ｃｈａｐｌｙｇｉｎ方程的合理过渡和从Ｃｈａｐｌｙｇｉｎ方程向Ｌｉｎｄｉｌｏｆ     

Lax方程组的求解公式

本文给出了一些著名的非线性演化方程的Ｌａｘ方程组求解公式．利用这些公式，只需算积分就能不断求得这些方程的解．从而提供了利用Ｌａｘ方程组求解非线性方程的新途径．     

The variational iteration method for analytic treatment for linear and nonlinear ODEs

In this work, the variational iteration method (VIM) is used for analytic treatment of the linear and nonlinear ordinary differential equations, homogeneous or inhomogeneous. The method is capable of reducing the size of calculations and handles both linear and nonlinear equations, homogeneous or inhomogeneous, in a direct manner. However, for concrete problems, a huge number of iterations are needed for a reasonable level of accuracy.     

常系数线性差分方程的微分解法

用微分方法 ,解常系数线性差分方程     

Oscillation and Nonoscillation Criteria for a Second Order Linear Equation

New oscillation and nonoscillation criteria are established for the equation

New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations

We give a substantially simplified proof of the near-optimal estimate on the Kuramoto-Sivashinsky equation from a previous paper of the third author, at the same time slightly improving the result. That result relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that in many ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified Kármán-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. We show that this provides a new interpretation of recent results obtained by Golse and Perthame.     

求解微分方程初值问题的一种弧长法

对于连续介质力学问题中导出的微分方程初值问题,常常具有解奇异性,如不连续、Ｓｔｉｆ性质或激波间断·本文通过在相应空间,引入一个或数个弧长参数变量,克服解的奇异性·对于常微分方程组引入弧长参数变量后,奇异性得以消除和削弱,应用一般的解常微分方程组的方法（如Ｒｕｎｇｅ＿Ｋｕｔａ法）求解·对于偏微分方程引入弧长参数变量后,在相应的空间离散成常微分方程组,用解奇异性常微分方程组相同的方法即可求解·本文给出了两个算例     

Symbolic computation of solutions for a forced Burgers equation

In this paper we give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method.     

Solutions for a class of iterated singular equations

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.     

Equilibration Rate for the Linear Inhomogeneous Relaxation-Time Boltzmann Equation for Charged Particles

Abstract

We study the long-time behavior of a linear inhomogeneous Boltzmann equation. The collision operator is modeled by a simple relaxation towards the Maxwellian distribution with zero mean and fixed lattice temperature. Particles are moving under the action of an external potential that confines particles, i.e., there exists a unique stationary probability density. Convergence rate towards global equilibrium is explicitly measured based on the entropy dissipation method and apriori time independent estimates on the solutions. We are able to prove that this convergence is faster than any algebraic time function, but we cannot achieve exponential convergence.     

On the coupling of BEM and FEM for exterior problems for the Helmholtz equation

This paper deals with the coupled procedure of the boundary element method (BEM) and the finite element method (FEM) for the exterior boundary value problems for the Helmholtz equation. A circle is selected as the common boundary on which the integral equation is set up with Fourier expansion. As a result, the exterior problems are transformed into nonlocal boundary value problems in a bounded domain which is treated with FEM, and the normal derivative of the unknown function at the common boundary does not appear. The solvability of the variational equation and the error estimate are also discussed.