Nonlocal problem with the integral condition for a loaded heate equation
M. M. Sagdullayeva
National University of Uzbekistan after named Mirzo Ulugbek
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.
non-local problem, integral condition, loaded equation, thermal conductivity, Green's function.
|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.
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MSC: Primary 35К10; Secondary 35К20
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
\paper Nonlocal problem with the integral condition for a loaded heate equation
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
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