Inverse problems of determining an unknown depending on time coefficient for a parabolic equation with involution and periodicity conditions

被引：1

作者：

Baranetskij, Ya. O. ^{[1
]}

Demkiv, I. I. ^{[1
]}

Solomko, A. V. ^{[2
]}

机构：

[1] Lviv Polytech Natl Univ, 12 Bandera str, UA-79013 Lvov, Ukraine

[2] Vasyl Stefanyk Precarpathian Natl Univ, 57 Shevchenka Str, UA-76018 Ivano Frankivsk, Ukraine

来源：

CARPATHIAN MATHEMATICAL PUBLICATIONS | 2023年 / 15卷 / 01期

关键词：

inverse problem; heat conduction equation; method of separation of variables; nonlocal condition; involution; Riesz basis; ORDINARY DIFFERENTIAL-OPERATORS; HEAT-EQUATION;

D O I：

10.15330/cmp.15.1.5-19

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The solution of the investigated problem with an unknown coefficient in the equation was con-structed by using the method of separation of variables. The properties of the induced spectral problem for the second-order differential equation with involution are studied. The dependence on the equation involutive part of the spectrum and its multiplicity as well as the structure of the sys-tem of root functions and partial solutions of the problem were investigated. The conditions for the existence and uniqueness of the solution of the inverse problem have been established. To determine the required coefficient, Volterra's integral equation of the second kind was found and solved.

引用

页码：5 / 19

页数：15

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