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 Vestnik KRAUNC. Fiz.-Mat. Nauki, 2021, Volume 34, Number 1, Pages 47–56 (Mi vkam454)

MATHEMATICS

Nonlocal problem with the integral condition for a loaded heate equation

M. M. Sagdullayeva

National University of Uzbekistan after named Mirzo Ulugbek

Abstract: In this paper, we consider a non-local problem with the integral condition for the loaded heat equation, where the loaded term is a derivative of the second order from an unknown function at the origin. The existence and uniqueness of a regular solution is proven. Using the Green's functions and thermal potentials, the existence of a regular solution to this problem is proved. The proof is based on the reduction of the formulated problem to the second kind Volterra integral equation with a weak singularity. The solvability of the obtained Volterra integral equations implies the existence of a unique solution to the problem.

Keywords: non-local problem, integral condition, loaded equation, thermal conductivity, Green's function.

 Funding Agency The name of the funding programme: This work was supported by the Ministry of Innovative Development of the Republic of Uzbekistan, grant OT — F4 — (36 + 32). Organization that has provided funding: Innovative Development of the Republic of Uzbekistan.

DOI: https://doi.org/10.26117/2079-6641-2021-34-1-47-56

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UDC: 517.956.4
MSC: Primary 35Ê10; Secondary 35Ê20

Citation: M. M. Sagdullayeva, “Nonlocal problem with the integral condition for a loaded heate equation”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 34:1 (2021), 47–56

Citation in format AMSBIB
\Bibitem{Sag21} \by M.~M.~Sagdullayeva \paper Nonlocal problem with the integral condition for a loaded heate equation \jour Vestnik KRAUNC. Fiz.-Mat. Nauki \yr 2021 \vol 34 \issue 1 \pages 47--56 \mathnet{http://mi.mathnet.ru/vkam454} \crossref{https://doi.org/10.26117/2079-6641-2021-34-1-47-56}