An inverse problem for a mixed-type equation in space
https://doi.org/10.25587/2411-9326-2025-4-101-111
Abstract
The paper investigates an inverse problem for a second-order parabolic equation in a two-dimensional domain with variable time direction. The objective is to determine an unknown source function together with the solution, subject to boundary, initial, final, and gluing conditions. The separation of variables method reduces the problem to a spectral formulation involving eigenvalues and eigenfunctions. Using orthogonality, explicit series expansions for the solution and source are derived. Convergence of the series is shown, while existence and uniqueness of a classical solution are established via functional analysis and the Hilbert–Schmidt theorem.
About the Authors
K. S. Fayazov
Turin Polytechnic University in Tashkent
Uzbekistan
Uzbekistan
Kudratillo S. Fayazov
17 Kichik Khalka Yuli Street, 100195 Tashkent
D. S. Juraeva
Turin Polytechnic University in Tashkent
Uzbekistan
Uzbekistan
Dildora S. Juraeva
17 Kichik Khalka Yuli Street, 100195 Tashkent
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Review
For citations:
Fayazov K.S., Juraeva D.S. An inverse problem for a mixed-type equation in space. Mathematical notes of NEFU. 2025;32(4):101-111. https://doi.org/10.25587/2411-9326-2025-4-101-111
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