Inverse Problems of Determination of the Time-Dependent Coefficient of a Parabolic Equation with Involution and Antiperiodicity Conditions

被引：0

作者：

Baranetskij Y.O. ^{[1
]}

Demkiv I.I. ^{[1
]}

Kaleniuk P.I. ^{[1
]}

机构：

[1] Lviv Polytechnic National University, Lviv

来源：

Journal of Mathematical Sciences | 2024年 / 282卷 / 5期

关键词：

heat-condition equation; inverse problem; involution; method of separation of variables; nonlocal conditions; Riesz basis;

D O I：

10.1007/s10958-024-07210-0

中图分类号：

学科分类号：

摘要：

By the method of separation of variables, we construct the solution of the investigated problem with an unknown coefficient in the differential equation. We study the properties of the spectral problem for the second-order differential equation with involution. The dependence of the spectrum of the operator of the problem, its multiplicity, and the structure of the system of root functions and particular solutions of the problem on the involutive part of the equation is analyzed. We establish the conditions for the existence and uniqueness of the solution to the inverse problem. To determine the unknown coefficient, we find and solve the Volterra integral equation of the second kind. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

引用

页码：699 / 717

页数：18

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