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Solvability of mixed problems for heat equations with two nonlocal conditions

  • Onur Alp İlhan EMAIL logo , Danyal Soybaş , Shakirbay G. Kasimov and Farhod D. Rakhmanov
Published/Copyright: December 4, 2022
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Abstract

In this study, the solvability of a problem of the heat conduction theory with two nonlocal boundary conditions is investigated. Systems of eigenfunctions of the corresponding operator with two nonlocal boundary conditions are taken into consideration. A theorem on the solvability of the problem of the theory of heat conduction with two nonlocal boundary conditions is given

MSC 2010: Primary 47A75; 58J35
  1. ( Communicated by Alberto Lastra )

References

[1] Bary, N. K: Biorthogonal systems and bases in Hilbert space, Uch. Zap. MGU, Matematika 148(4) (1951), 69–107.Search in Google Scholar

[2] Cannon, J. R.: The solution of heat equation subject to the specification of energy, Quart. Appl. Math. 21(2) (1963), 155–160.10.1090/qam/160437Search in Google Scholar

[3] İlhan, O. A.–-Kasimov, Sh. G.–-Rakhmanov, F. D.–-Baskonus, H. M.: On the solvability of a problem of the heat conduction theory with two nonlocal conditions. Abstract Book of the 4th International Conference on Computational Mathematics and Engineering Sciences, April, 2019Search in Google Scholar

[4] Il’in, V. A.: On the solvability of mixed problems for hyperbolic and parabolic equations, Uspekhi Mat. Nauk. 15(2) (1960), 97–154.10.1070/RM1960v015n02ABEH004217Search in Google Scholar

[5] Il’in, V. A.: Necessary and sufficient conditions for a subsystem of the eigen- and associated functions of a Keldys bundle of ordinary differential operators to be a basis, Dokl. Akad. Nauk SSSR 227 (1976), 796–799, Engl. transl.: Soviet Math. Dokl. 17 (1976), 513–516.Search in Google Scholar

[6] Ionkin, N. I.: The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition, Differ. Uravn. 13(2) (1977), 294–304.Search in Google Scholar

[7] Kasimov, S. G.–-Rakhmanov, F. D.: On a spectral problem of the heat conduction theory with nonlocal boundary conditions, Tashkent Vestnik NUUz 2 (2013), 83–86.Search in Google Scholar

[8] Kasimov, S. .G.–-Rakhmanov, F. D.: On a spectral problem of the heat conduction theory with nonlocal boundary conditions of the Samarskii-Ionkin type, Tashkent Vestnik NUUz 1–2 (2014).Search in Google Scholar

[9] Naimark, M. A.: Linear Differential Operators, Nauka, Moscow, 1969.Search in Google Scholar

[10] Tikhonov, A. N.–-Samarskii, A. A.: Equations of Mathematical Physics, Nauka, Moscow, 1977.Search in Google Scholar

Received: 2021-05-27
Accepted: 2021-10-15
Published Online: 2022-12-04
Published in Print: 2022-12-16

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