Geodesic
Nonlocal problem with the integral condition for a loaded heate equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 47-56

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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. 
@article{VKAM_2021_34_1_a3,
     author = {M. M. Sagdullayeva},
     title = {Nonlocal problem with the integral condition for a loaded heate equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {47--56},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2021_34_1_a3/}
}
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M. M. Sagdullayeva. Nonlocal problem with the integral condition for a loaded heate equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 47-56. http://geodesic.mathdoc.fr/item/VKAM_2021_34_1_a3/