One-dimensional inverse problems of determining the kernel of the integro-differential heat equation in a bounded domain
D. K. DurdievBukhara Branch of the Institute of Mathematics named after V.I. Romanovskiy Academy of Sciences of the Republic of Uzbekistan , Bukhara , UzbekistanJ. J. JumaevDepartment of Differential Equations, Bukhara State University , Bukhara 200100 , Uzbekistan
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Abstract
Abstract The integro-differential equation of heat conduction with the time-convolution integral on the right side is considered. The direct problem is the initial-boundary problem for this integro-differential equation. Two inverse problems are studied for this direct problem consisting in determining a kernel of the integral member on two given additional conditions with respect to the solution of the direct problems, respectively. The problems are replaced with the equivalent system of the integral equations with respect to unknown functions and on the basis of contractive mapping the unique solvability inverse problem.
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