Linear identifications problems for singular integro-differential equations of Gerasimov type
https://doi.org/10.25587/2411-9326-2025-1-46-64
Abstract
The issues of unique solvability of linear inverse coefficient problems for evolution integro-differential equations of Gerasimov type with a singular integral kernel in Banach spaces are investigated. The cases of bounded and sectorial operators at the unknown function in the equation are considered. In each case, correctness criteria were obtained for the linear inverse problem with a time-independent unknown coefficient, and sufficient conditions for solvability and correctness estimates were found for the linear identification problem with a time-dependent unknown coefficient. The abstract results obtained are illustrated by an example of a class of inverse problems for partial differential equations.
About the Authors
V. E. Fedorov
Mathematical Analysis Department, 447, Chelyabinsk State University
Russian Federation
Russian Federation
Vladimir E. Fedorov
Kashirin Brothers St., 129, Chelyabinsk 454001
D. V. Melekhina
Mathematical Analysis Department, 447, Chelyabinsk State University; Yugra State University
Russian Federation
Russian Federation
Darya V. Melekhina
Kashirin Brothers St., 129, Chelyabinsk 454001;
16 Chekhov Street, Khanty-Mansiysk 628012,
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Review
For citations:
Fedorov V.E., Melekhina D.V. Linear identifications problems for singular integro-differential equations of Gerasimov type. Mathematical notes of NEFU. 2025;32(1):46-64. (In Russ.) https://doi.org/10.25587/2411-9326-2025-1-46-64
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