Inner boundary value problem with displacement for a second order mixed parabolic-hyperbolic equation

被引：1

作者：

Balkizov, Zh A. ^{[1
]}

Guchaeva, Z. Kh ^{[2
]}

Kodzokov, A. Kh ^{[2
]}

机构：

[1] KBSC RAS, Inst Appl Math & Automat, Nalchik, Russia

[2] Kabardino Balkarian State Univ, Nalchik, Russia

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2022年 / 106卷 / 02期

关键词：

wave equation; degenerate hyperbolic equation of the first kind; Volterra integral equation; Fredholm integral equation; Tricomi method; method of integral equations; methods of fractional calculus theory;

D O I：

10.31489/2022M2/59-71

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates inner boundary value problems with a shift for a second-order mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic operator of the first kind in the other part. We find sufficient conditions for the given functions to ensure the existence of a unique regular solution to the problems under study. In some special cases, solutions are obtained explicitly.

引用

页码：59 / 71

页数：13

共 50 条

[1] A BOUNDARY VALUE PROBLEM FOR A MIXED PARABOLIC-HYPERBOLIC TYPE OF EQUATION
BZHIKHAT.KG
NAKHUSHE.AM
[J]. DOKLADY AKADEMII NAUK SSSR, 1968, 183 (02): : 261 - &
[2] Nonlocal Boundary-Value Problem for a Parabolic-Hyperbolic Equation of the Second Kind
Urinov, A. K.
Okboev, A. B.
[J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2020, 41 (09) : 1886 - 1897
[3] Nonlocal Boundary-Value Problem for a Parabolic-Hyperbolic Equation of the Second Kind
A. K. Urinov
A. B. Okboev
[J]. Lobachevskii Journal of Mathematics, 2020, 41 : 1886 - 1897
[4] Boundary Value Problems for a Mixed Equation of Parabolic-Hyperbolic Type of the Third Order
Yu. P. Apakov
A. A. Sopuev
[J]. Lobachevskii Journal of Mathematics, 2023, 44 : 5155 - 5163
[5] On a new nonlocal boundary value problem for an equation of the mixed parabolic-hyperbolic type
Dildabek, Gulnar
[J]. APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'16), 2016, 1789
[6] Boundary Value Problems for a Mixed Equation of Parabolic-Hyperbolic Type of the Third Order
Apakov, Yu. P.
Sopuev, A. A.
[J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2023, 44 (12) : 5155 - 5163
[7] Tricomi Problem for Mixed Parabolic-Hyperbolic Equation with Higher Order Boundary Condition
Derbissaly, Bauyrzhan
Sadybekov, Makhmud
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2023, 49 (04)
[8] The first boundary value problem with deviation from the characteristics for a second-order parabolic-hyperbolic equation
Balkizov, Zh A.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018, 90 (02): : 34 - 42
[9] On a nonlocal boundary value problem for parabolic-hyperbolic type equation
Karahan, Done
Mamedov, Hanlar R.
[J]. NOTE DI MATEMATICA, 2023, 43 (01): : 57 - 65
[10] THE BOUNDARY VALUE PROBLEM FOR THE LOADED EQUATION OF MIXED PARABOLIC-HYPERBOLIC TYPE IN RECTANGULAR AREA
Tarasenko, A. V.
[J]. VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2010, (05): : 263 - 267

← 1 2 3 4 5 →