二阶线性抛物型方程利用线性变换求解定理  

The Solving Theorem of Second Order Linear Parabolic Equation Utilizing Linear Transformation

作　　者：刘许成[1] 

机构地区：[1]潍坊学院,山东潍坊261041

出　　处：《潍坊学院学报》2005年第2期84-85,共2页Journal of Weifang University

基　　金：潍坊学院自然科学基金资助项目。

摘　　要：对于二阶项系数a,b,c为常数的二个自变量的二阶线性抛物型方程au_(xx)+2bu_(xy)+cu_(yy)+du_x+eu_y+g=0,当系数d,e满足一定条件时,可以利用线性变换T:ξ=a_(11)x+a_(12)y,η=a_(21)x+a_(22)y化为一阶线性常微分方程求解,本文给出了判别定理和求解方法。To the second order linear parabolic equation with two independent variables au_(xx)+2bu_(xy)+cu_(yy)+du_(x)+eu_(y)+g=0 when its coefficients a, b, c are constants and d, e satisfy given conditions,we may utilize the transformation T:ξ=a_(11)x+a_(12)y,η=a_(21)x+a_(22)y to make it as first order linear ordinary differential equation for solving. At the same time, we give the discrimination theorem and application method.

关 键 词：二阶线性抛物型方程 线性变换 特征方程 判别定理 

分 类 号：O175.26[理学—数学]