On a boundary value problem for the heat equation and a singular integral equation associated with it

被引：6

作者：

Amangaliyeva, Meiramkul ^{[1
]}

Jenaliyev, Muvasharkhan ^{[1
]}

Iskakov, Sagyndyk ^{[2
]}

Ramazanov, Murat ^{[2
]}

机构：

[1] Inst Math & Math Modeling, Dept Differential Equat, Pushkin Str 25, Alma Ata 050010, Kazakhstan

[2] Buketov Karaganda State Univ, Dept Math & Informat Technol, Univ Skaya Str 28, Karaganda 100028, Kazakhstan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 399卷

关键词：

Heat equation; Degenerate domain; Volterra integral equation; Singular integral equation; Integral operator; Resolvent;

D O I：

10.1016/j.amc.2021.126009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the solvability of a singular integral equation arising in the theory of boundary value problems for the heat equation in an infinite angular domain. The particular case of the corresponding homogeneous integral equation was investigated earlier in [1, 2] and it was shown that in a weight class of essentially bounded functions it has, along with a trivial solution, a family of non-trivial solutions up to a constant factor. In this paper we study the more general case of a nonhomogeneous integral equation for which a representation of the general solution is found with using the resolvent constructed by us. Estimates of the resolvent and of the solution of the boundary value problem are established. (C) 2021 Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of Republic of Kazakhstan. Published by Elsevier Inc.

引用

页数：14

共 17 条

[1] On one homogeneous problem for the heat equation in an infinite angular domain [J].

Amangalieva, M. M. ;

Dzhenaliev, M. T. ;

Kosmakova, M. T. ;

Ramazanov, M. I. .

SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (06) :982-995

[2]

Brychkov Y.A., 2003, INTEGRALS SERIES, V2, P664

[3]

Gradshtein I.S., 2007, Table of integrals, series, and Products, V7th

[4] The Resolvent and the Particular Solution of One Singular Integral Equation [J].

Jenaliyev, Muvasharkhan ;

Iskakov, Sagyndyk ;

Ramazanov, Murat .

INTERNATIONAL CONFERENCE FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS (FAIA2017), 2017, 1880

[5] On a homogeneous parabolic problem in an infinite corner domain [J].

Jenaliyev, Muvasharkhan ;

Ramazanov, Murat .

INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016), 2016, 1759

[6] On a Volterra equation of the second kind with 'incompressible' kernel [J].

Jenaliyev, Muvasharkhan ;

Amangaliyeva, Meiramkul ;

Kosmakova, Minzilya ;

Ramazanov, Murat .

ADVANCES IN DIFFERENCE EQUATIONS, 2015,

[7] About Dirichlet boundary value problem for the heat equation in the infinite angular domain [J].

Jenaliyev, Muvasharkhan He ;

Amangaliyeva, Meiramkul ;

Kosmakova, Minzilya ;

Ramazanov, Murat .

BOUNDARY VALUE PROBLEMS, 2014, :1-21

[8]

Kheloufi A, 2010, DIFFER EQUAT APPL, V2, P251

[9]

Kheloufi A., 2016, ARAB J MATH SCI, V22, P165, DOI [10.1016/j.ajmsc.2015.06.002, DOI 10.1016/J.AJMSC.2015.06.002]

[10] Existence and uniqueness results for parabolic equations with Robin type boundary conditions in a non-regular domain of R3 [J].

Kheloufi, Arezki .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 220 :756-769

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