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Uzbekistan Bukhara; Tashkent
Year
2023
Volume
33
Issue
1
Pages
90-102
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Section Mathematics
Title Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition
Author(-s) Durdiev D.K.ab, Jumaev J.J.b, Atoev D.D.a
Affiliations Bukhara State Universitya, Institute of Mathematics, National Academy of Sciences of Uzbekistanb
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
UDC 517.958
MSC 35K60, 35R30, 45G15
DOI 10.35634/vm230106
Received 20 December 2022
Language English
Citation Durdiev D.K., Jumaev J.J., Atoev D.D. Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 1, pp. 90-102.
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