Zh. Zh. Zhumayev

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Articles: 1

Problem of determining a multidimensional thermal memory in a heat conductivity equation

D. K. Durdiev, Zh. Zh. Zhumayev

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 25 (2019), no. 3, 219-226

We consider a multidimensional integro-differential equation of heat conductivity with time-convolution integral in the right hand-side. The direct problem is represented by the Cauchy problem of determining the temperature of the medium for a known initial distribution of heat. We study the inverse problem of determining the kernel, in the integral part, that depends on time and spatial variables, if a solution of the direct problem is known on the hyperplane $x_n=0$ for $t>0.$ With a use of the resolvent of the kernel, this problem is reduced to a study of a more convenient inverse problem. The later problem is replaced with an equivalent system of integral equations with respect to the unknown functions and, using a contractive mapping, we prove that the direct and the inverse problems have unique solutions.


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