This article is devoted to the issue of identifying initial conditions in an inverse heat conduction problem related to the challenge of determining the initial thermal state of a technical object. The article proposes an approach to identifying the initial conditions via reducing the original problem to an integral equation describing a direct relationship between the unknown function of the initial condition and the given boundary conditions. A regularizing numerical algorithm has been developed to solve the integral equation. The proposed approach to solving the problem of identifying initial conditions extends the results obtained for the boundary value inverse heat conduction problem and the internal thermal source identification problem to a new class of inverse problems.
Keywords: identification, initial conditions, information processing method, integral equation, inverse problem, regularization, numerical method
Received January 23, 2026
Revised February 2, 2026
Accepted February 9, 2026
Natalia Mikchailovna Yaparova, Dr. Tehn. Sci., South Ural State University (NRU), Chelyabinsk, 454080 Russia, e-mail: natyap7@mail.ru
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Cite this article as: N.M. Yaparova. On identification of initial conditions in the inverse heat conduction problem. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 1, pp. 286–295.
