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This article is cited in 1 scientific paper (total in 2 paper)
MATHEMATICS
Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition
D. K. Durdieva, J. J. Jumayeva, D. D. Atoevb a Bukhara Branch of
the Institute of Mathematics named after V. I. Romanovskiy at the Academy of Sciences of the Republic
of Uzbekistan, ul. M. Ikbal, 11, Bukhara, 200118, Uzbekistan
b Bukhara State University, ul. M. Ikbal, 11, Bukhara, 200118,
Uzbekistan
Abstract:
In this paper, an inverse problem for a one-dimensional integro-differential heat equation is investigated with nonlocal initial-boundary and integral overdetermination conditions. We use the Fourier method and the Schauder principle to investigate the solvability of the direct problem. Further, the problem is reduced to an equivalent closed system of integral equations with respect to unknown functions. Existence and uniqueness of the solution of the integral equations are proved using a contractive mapping. Finally, using the equivalency, the existence and uniqueness of the classical solution is obtained.
Keywords:
integro-differential equation, nonlocal initial-boundary problem, inverse problem, integral equation, Schauder principle.
Received: 20.11.2022 Accepted: 18.01.2023
Citation:
D. K. Durdiev, J. J. Jumayev, D. D. Atoev, “Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 90–102
Linking options:
https://www.mathnet.ru/eng/vuu837 https://www.mathnet.ru/eng/vuu/v33/i1/p90
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