[1]王元明.一类三阶线性偏微分方程Reimann函数正定性及极值原理[J].东南大学学报(自然科学版),1965,7(1):61-68.[doi:10.3969/j.issn.1001-0505.1965.01.004]
 Wang Yuan Ming.The positive Definite property of Reimann’s function and A Maximum Principle for a class of linear partial Differential equations of the third order[J].Journal of Southeast University (Natural Science Edition),1965,7(1):61-68.[doi:10.3969/j.issn.1001-0505.1965.01.004]
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一类三阶线性偏微分方程Reimann函数正定性及极值原理()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
7
期数:
1965年第1期
页码:
61-68
栏目:
本刊信息
出版日期:
1965-03-20

文章信息/Info

Title:
The positive Definite property of Reimann’s function and A Maximum Principle for a class of linear partial Differential equations of the third order
作者:
王元明
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Author(s):
Wang Yuan Ming
关键词:
极值原理 正定性 函数定义 二阶双曲型方程 线性偏微分方程 建立方程 定理 极植原理 三阶 满足条件
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1965.01.004
摘要:
在本文中我们考虑了如方程:u_{xyz}-a(x)u_{yz}-b(y)u_{zx}-c(z)u-(xy)-d(y.z)u_x-e(x.z)u_y-f(x.y)u_z-g(x.y.z)u=0 (1)的极值原理。所获得的结果表明:如果方程(1)的系数满足某些条件,则柯西问题与混合问题的极值原理成立。二阶双曲型方程类似的极值原理已被一些作者研究过了(见为了证明极值原理,我们需要建立 Reimann 函数的正定性。在§1中我们讨论了这个性质,在§2与§3中我们利用在§1中已获得的结果证明了极值原理。
Abstract:
In this paper we consider a maximum principle of differential equation of the form: u_{xyz}-a(x)u_{yz}-b(y)_{zx}-c(z)u_{xy}-d(y,z)u_x -e(x,z)u_y-f(x,y)u_z-g(x,y,z)u=0 (1) Obtained results show:If Coefficients of equation (1) satisfy some conditions, then maximum principle of Cauchy’s problem and mixed problem hold. The same principle for second order hyperbolic equation was proved by several Authors.(see [1]-[5]) In order to prove a maximum principle we have to establish the positive de- finite property of Reimann’s function.In section 1 of this paper we discuss this property.In section 2 and 3,with the help of results obtained in section 1 we prove a maximum principle.
更新日期/Last Update: 2013-05-01