Vestnik КRAUNC. Fiz.-Mat. Nauki. 2026. vol. 54. no. 2. P. 10 – 25. ISSN 2079-6641

MATHEMATICS
https://doi.org/10.26117/2079-6641-2026-54-2-10-25
Research Article
Full text in English
35A01, 35A02, 35L02, 35L03, 35R03

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Global Solvability of the Inverse Problem of Determining the Kernel for a Pseudoparabolic Equation with Overdetermination at an Interior Point

B. S. Ablabekov¹^{\ast}, K. B. Matanova²

¹Kyrgyz National University named after Zhusup Balasagyn, 720033, 547 Frunze str., Bishkek, Kyrgyzstan
²Kyrgyz-Turkish Manas University, 720038, 56 prosp. Chyngyza Aitmatova, Bishkek, Kyrgyzstan

Abstract. This paper considers the inverse problem of determining the kernel of the integral term in an integro-differential pseudoparabolic equation with distributed data over a bounded domain. First, the direct problem is studied. The direct problem represents the first initial-boundary value problem for this integrodifferential equation. For this direct problem, the inverse problem is studied, which consists of determining the kernel of the integral under a given additional condition regarding the solution of the direct problem. Using the semi-inversion method, this problem is replaced by an equivalent system of integral equations for the unknown functions, and, based on a contraction mapping, the global unique solvability of this inverse problem in the space of continuous functions with weighted norms is proved.

Key words: pseudoparabolic equation, integro-differential equation, inverse problem, semi-inversion
method, contraction mapping principle.

Received: 08.05.2026; Revised: 19.06.2026; Accepted: 15.08.2026; First online: 14.09.2026

For citation. Ablabekov B. S., Matanova K. B. Global solvability of the inverse problem of determining the kernel for a pseudoparabolic equation with overdetermination at an interior point. Vestnik KRAUNC. Fiz.-mat. nauki. 2026, 54: 2, 10-25. EDN: PDVNRC. https://doi.org/10.26117/2079-6641-2026-54-2-10-25.

Funding. This work was not supported by any external funding.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: ablabekov_63@mail.ru, matanova@manas.edu.kg

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Ablabekov B. S., Matanova K. B., 2026

© Institute of Cosmophysical Research and Radio Wave Propagation, 2026 (original layout, design, compilation)

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