On Solvability of Some Inverse Problems for a Pseudoparabolic Equation with Multiple Involution

Maira Koshanova, Kulzina Nazarova (), Batirkhan Turmetov and Kairat Usmanov
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Maira Koshanova: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
Kulzina Nazarova: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
Batirkhan Turmetov: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
Kairat Usmanov: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan

Mathematics, 2025, vol. 13, issue 16, 1-15

Abstract: In this paper, solvability of some inverse problems for a nonlocal analog of a pseudoparabolic equation is studied. The nonlocal analog of a pseudoparabolic equation is formed using transformations that have the involution property. Two types of inverse problems are considered. In the first problem, in addition to the solution, a function in the right-hand side of the equation depending on the spatial variable is determined. In the second problem, a function depending on the time variable is found. The first problem is solved using the Fourier method, and the second problem is solved by reducing to the integral Volterra equation.

Keywords: involution; nonlocal equation; pseudoparabolic equation; inverse problem; Fourier method; Volterra equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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