Third Boundary Value Problem for an Equation with the Third Order Multiple Characteristics in Three Dimensional Space

被引：2

作者：

Apakov, Yu. P. ^{[1
,2
]}

Hamitov, A. A. ^{[2
]}

机构：

[1] Acad Sci Uzbek, Romanovskii Inst Math, Tashkent 100174, Uzbekistan

[2] Namangan Engn Construct Inst, Namangan 160103, Uzbekistan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 02期

关键词：

partial differential equation; third order equation; multiple characteristics; boundary value problem; uniqueness; existence; series; absolute and smooth convergence; PARTIAL INTEGRODIFFERENTIAL EQUATION; DIRICHLET PROBLEM;

D O I：

10.1134/S1995080223020099

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, the third boundary value problem for an equation with the third order multiple characteristics in three dimensional space is studied. Uniqueness of the solution of the given problem is proved by the method of energy integral. Existence of the solution is proved by means of the method of variables separation. The solution is constructed in the exact infinite series form and an opportunity of term-by-term differentiation is justified. It is important in smooth convergence of the series, that ''small denominator'' is different from zero.

引用

页码：523 / 532

页数：10

共 50 条

[1] Third Boundary Value Problem for an Equation with the Third Order Multiple Characteristics in Three Dimensional Space
Yu. P. Apakov
A. A. Hamitov
Lobachevskii Journal of Mathematics, 2023, 44 : 523 - 532
[2] Third Boundary-Value Problem for a Third-Order Differential Equation with Multiple Characteristics
Yu. P. Apakov
A. Kh. Zhuraev
Ukrainian Mathematical Journal, 2019, 70 : 1467 - 1476
[3] Third Boundary-Value Problem for a Third-Order Differential Equation with Multiple Characteristics
Apakov, Yu. P.
Zhuraev, A. Kh.
UKRAINIAN MATHEMATICAL JOURNAL, 2019, 70 (09) : 1467 - 1476
[4] On the solution of a boundary-value problem for a third-order equation with multiple characteristics
Yu. P. Apakov
Ukrainian Mathematical Journal, 2012, 64 : 1 - 12
[5] On the solution of a boundary-value problem for a third-order equation with multiple characteristics
Apakov, Yu P.
UKRAINIAN MATHEMATICAL JOURNAL, 2012, 64 (01) : 1 - 12
[6] On a boundary value problem to third order PDE with multiple characteristics
Apakov, Yusufjon P.
Rutkauskas, Stasys
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2011, 16 (03): : 255 - 269
[7] On problem for a third order equation with multiple characteristics
Abdinazarov, S
Kholboev, BM
ILL-POSED AND NON-CLASSICAL PROBLEMS OF MATHEMATICAL PHYSICS AND ANALYSIS, PROCEEDINGS, 2003, : 173 - 178
[8] On solution of the boundary value problems posed for an equation with the third-order multiple characteristics in semi-bounded domains in three dimensional space
Yu. P. Apakov
A. A. Hamitov
Boletín de la Sociedad Matemática Mexicana, 2023, 29
[9] On solution of the boundary value problems posed for an equation with the third-order multiple characteristics in semi-bounded domains in three dimensional space
Apakov, Yu. P.
Hamitov, A. A.
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2023, 29 (03):
[10] Boundary-value problem with saigo operators for mixed type equation of the third order with multiple characteristics
Repin O.A.
Kumykova S.K.
Russian Mathematics, 2015, 59 (7) : 44 - 51

← 1 2 3 4 5 →