| 二阶常系数线性偏微分方程求解定理 |
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| 引用本文： | 李志强,王显春,钟太勇. 二阶常系数线性偏微分方程求解定理[J]. 合肥学院学报(自然科学版), 2008, 18(1): 25-28 |
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| 作者姓名： | 李志强 王显春 钟太勇 |
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| 作者单位： | 云南民族大学,数学与计算机科学学院,昆明,650031;云南民族大学,数学与计算机科学学院,昆明,650031;郧阳师范高等专科学校,数学系,湖北,十堰,442000 |
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| 摘 要： | 两个自变量的二阶常系数偏微分方程auxx＋2buxy＋cuyy＋dux＋euy＋g=0,当系数满足一定条件时，可利用变换T：ξ=φ（x,y）,η=Ф（x,y）化为简单微分方程求解，结合所定条件给出了判定定理和应用方法．
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| 关 键 词： | 偏微分方程 特征线 特征方程 |
| 文章编号： | 1673-162X(2008)01-0025-04 |
| 修稿时间： | 2007-08-31 |
The Solving Theorem of Second Order Constant Coefficient Linear Partial Differential Equation |
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| LI Zhi-qiang,WANG Xian-chun,ZHONG Tai-yong. The Solving Theorem of Second Order Constant Coefficient Linear Partial Differential Equation[J]. Journal of Hefei University(Natural Sciences Edition), 2008, 18(1): 25-28 |
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| Authors: | LI Zhi-qiang WANG Xian-chun ZHONG Tai-yong |
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| Affiliation: | LI Zhi-qiang , WANG Xian-chun , ZHONG Tai-yong ( 1. School of Mathematics and Computer Science,Yunnan Nationalities University, Kunming 650031 ; 2. Department of Mathematics, Yunyang Teacher＇s College, Shiyan, Hubei 442000, China) |
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| Abstract: | Abstract：There is the second order constant coefficient linear patial differential equation with two variables auxx＋2buxy＋cuyy＋dux＋euy＋g=0. When its coefficients satisfy given conditions, we can utilize the transformations T：ξ=φ（x,y）,η=Ф（x,y） to make it as first simple ordinary differential equation for solving. At the same time, we give the discrimination theorem and application method. |
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| Keywords: | partial differential equation eigenline eigenequation |
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