[1]王元明.一类三阶线性偏微分方程奇性定解问题的显式解[J].东南大学学报(自然科学版),1982,12(1):1-11.[doi:10.3969/j.issn.1001-0505.1982.01.001]
 Wang Yuan-ming.Explicit Solutions of the Singular Problems for a Linear Partial Differential Equation of Third Order[J].Journal of Southeast University (Natural Science Edition),1982,12(1):1-11.[doi:10.3969/j.issn.1001-0505.1982.01.001]
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一类三阶线性偏微分方程奇性定解问题的显式解()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
12
期数:
1982年第1期
页码:
1-11
栏目:
本刊信息
出版日期:
1982-03-20

文章信息/Info

Title:
Explicit Solutions of the Singular Problems for a Linear Partial Differential Equation of Third Order
作者:
王元明
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Author(s):
Wang Yuan-ming
关键词:
定解问题 柯西问题 列方程 表达式 奇性 函数 系数 三阶 线性偏微分方程 满足条件
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1982.01.001
摘要:
本文研究了下列三阶Fuchs型方程: U_{xyz}+a/(x+y+z)U_{yz}+a/(x+y+z)U_{2x}+c/(x+y+z)U_{xy}+d/(x+y+z)^2U_x +e/(x+y+z)^2-U_y+f(x+y+z)^2U_z+g/(x+y+z)^3U=0 (1)(其中a,b,c……,g均为常数) 的奇柯西问题、奇第三问题及奇第四问题。当方程(1)的系数满足一定关系时,证明这些问题是适定的,并给出了解的表达式。当(1)的系数不满足上述关系时,我们对一个较简单的方程(33),通过Riemann公式建立了其柯西问题解的表达式。
Abstract:
In this paper we study the singular Cauchy’s problem, the singular third problem and the singular fourth problem for the following Fuchsisan equaton U_{xyz}+a/(x+y+z)U_{yz}+a/(x+y+z)U_{2x}+c/(x+y+z)U_{xy}+d/(x+y+z)^2U_x +e/(x+y+z)^2-U_y+f(x+y+z)^2U_z+g/(x+y+z)^3U=0 (1) (where a, b, c, ......, g are all contants). When the coefficients of the equation satisfy certain conditons, we prove that these problems are "correctly set", and give the explicit expressions of their solutons. When the coefficients of (1) do not satisfy the above-mentioned conditions, we consider only equation (33) which is a particular case of equation (1). A solution of cauchy’s problem for (33) is presented in terms of Riemann’s function.

相似文献/References:

[1]徐承龙.一类重特征偏微分方程的可解性[J].东南大学学报(自然科学版),1987,17(2):126.[doi:10.3969/j.issn.1001-0505.1987.02.014]
 Xu Chenglong(Departmen of Mathematics and Mechanics).The Solvability for a Class of Partial Diffferential Eqnatious with Double Characteristies[J].Journal of Southeast University (Natural Science Edition),1987,17(1):126.[doi:10.3969/j.issn.1001-0505.1987.02.014]

更新日期/Last Update: 2013-05-01