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

2024;
: pp. 1221–1232
https://doi.org/10.23939/mmc2024.04.1221
Received: December 22, 2022
Revised: November 20, 2024
Accepted: December 10, 2024

Baranetskij Ya. O., Demkiv I. I.  Inverse problems of determining an unknown coefficient depending on time for a parabolic equation with involution and anti-periodicity conditions.  Mathematical Modeling and Computing. Vol. 11, No. 4, pp. 1221–1232 (2024)

1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

Inverse problems of determining an unknown depending on time coefficient for a parabolic equation with involution and anti-periodicity conditions.  The solution of the investigated problem with an unknown coefficient in the equation was constructed 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 of the spectrum and its multiplicity and the structure of the system of root functions and partial solutions to the problem on the involutive part of this equation was studied.  The conditions for the existence and uniqueness of the solution to the inverse problem have been established.  To determine the required coefficient, Voltaire's integral equation of the second kind was found and solved.

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