The solution of the Cauchy problem for generalized Euler-Poisson-Darboux equation

被引：0

作者：

Hasanov, Anvar ^{[1
]}

机构：

[1] Uzbek Acad Sci, Inst Math, 29 F Hodjaev St, Tashkent 700125, Uzbekistan

来源：

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS | 2007年 / 8卷 / M07期

关键词：

Generalized Euler-Poisson-Darboux equation; degenerating hyperbolic type equations; function of Riemann; a Cauchy problem; confluent hypergeometric functions of Kummer from three variables;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper in a characteristic triangle Cauchy problem for generalized Euler-Poisson-Darboux equation L-alpha,L-beta (u) equivalent to u(xi eta) + [alpha/eta+xi + beta/eta-xi] u(xi) + [alpha/eta+xi - beta/eta-xi] u(eta) + gamma u = 0. is considered. Function of Riemann, which expressed by Kummer's function of three variables is constructed in an explicit form. By the method of Riemann for the hyperbolic equations, a solution of the Cauchy problem for generalized Euler-Poisson-Darboux equation expressed in an explicit form.

引用

页码：30 / 43

页数：14

共 50 条

[21] A SOLUTION OF THE SINGULAR INITIAL VALUE PROBLEM FOR THE EULER-POISSON-DARBOUX EQUATION
DIAZ, JB
WEINBERGER, HF
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (05) : 703 - 715
[22] A SOLUTION OF A SINGULAR MIXED PROBLEM FOR EQUATION OF EULER-POISSON-DARBOUX(EPD)
FUSARO, BA
AMERICAN MATHEMATICAL MONTHLY, 1966, 73 (06): : 610 - &
[23] A SOLUTION OF THE SINGULAR INITIAL VALUE PROBLEM FOR THE EULER-POISSON-DARBOUX EQUATION
DIAZ, JB
WEINBERGER, HF
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 59 (01) : 43 - 43
[24] ON EULER-POISSON-DARBOUX EQUATION
ERDELYI, A
JOURNAL D ANALYSE MATHEMATIQUE, 1970, 23 : 89 - &
[25] SOLUTION OF MIXED EPD SINGULAR PROBLEM FOR EQUATION OF EULER-POISSON-DARBOUX
FUSARO, BA
AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (07): : 832 - &
[26] PARTICULAR SOLUTIONS OF GENERALIZED EULER-POISSON-DARBOUX EQUATION
Seilkhanova, Rakhila B.
Hasanov, Anvar H.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[27] HUYGENS PRINCIPLE FOR A GENERALIZED EULER-POISSON-DARBOUX EQUATION
NISHIWADA, K
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1984, 60 (06) : 197 - 200
[28] An operator approach to the Cauchy problem for the Euler-Poisson-Darboux equation in spaces of constant curvature
Olevskii, MN
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2004, 49 (01) : 77 - 109
[29] A REMARK ON SINGULAR CAUCHY PROBLEM FOR ALL VALUES OF TIME FOR EULER-POISSON-DARBOUX EQUATION
DIAZ, JB
KIWAN, AR
JOURNAL OF MATHEMATICS AND MECHANICS, 1966, 16 (03): : 197 - &
[30] An Operator Approach to the Cauchy Problem for the Euler-Poisson-Darboux Equation in Spaces of Constant Curvature
M. N. Olevskii
Integral Equations and Operator Theory, 2004, 49 : 77 - 109

← 1 2 3 4 5 →