Geodesic
Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 90-102

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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. 
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     title = {Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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D. K. Durdiev; J. J. Jumayev; D. D. Atoev. Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 90-102. http://geodesic.mathdoc.fr/item/VUU_2023_33_1_a5/