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


  • Ya.O. Baranetskij Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • I.I. Demkiv Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • A.V. Solomko Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine


inverse problem, heat conduction equation, method of separation of variables, nonlocal condition, involution, Riesz basis
Published online: 2023-03-27


The solution of the investigated problem with an unknown coefficient in the equation was constructed 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 system 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.

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How to Cite
Baranetskij, Y.; Demkiv, I.; Solomko, A. Inverse Problems of Determining an Unknown Depending on Time Coefficient for a Parabolic Equation With Involution and Periodicity Conditions. Carpathian Math. Publ. 2023, 15, 5-19.

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