Affiliation:
1. Bukhara Branch of the Institute of Mathematics named after V.I. Romanovskiy at the Academy of Sciences of the Republic of Uzbekistan
2. Bukhara State University
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.
Subject
Fluid Flow and Transfer Processes,General Mathematics,General Computer Science
Cited by
1 articles.
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