69143e36-351d-4d06-b84a-5e61020715ea20220309090546579naun:naunmdt@crossref.orgMDT DepositInternational Journal of Geology1998-449910.46300/9105http://www.naun.org/cms.action?id=28303920223920221610.46300/9105.2022.16https://npublications.com/journals/geology/2022.phpG.MeladzeSaint Andrew the first-called Georgian University at Patriarchate of Georgia, Tbilisi, GeorgiaD.DevadzeDepartment of Computer Science, Batumi Shota Rustaveli State University, Batumi, GeorgiaV.BeridzeDepartment of Computer Science, Batumi Shota Rustaveli State University, Batumi, GeorgiaThe paper deals with optimal control problems whose behavior is described by an elliptic equations with Bitsadze– Samarski nonlocal boundary conditions. The theorem about a necessary and sufficient optimality condition is given. The existence and uniqueness of a solution of the conjugate problem are proved. A numerical method of the solution of an optimal problem by means of the Mathcad package is presented.392022392022141https://npublications.com/journals/geology/2022/a022004-001(2022).pdf10.46300/9105.2022.16.1https://npublications.com/journals/geology/2022/a022004-001(2022).pdfV. V. Shelukhin, A non-local in time model for radionuclides propagation in Stokes fluid. Dinamika Sploshn. Sredy No. 107 (1993), 180–193, 203, 207. 10.1006/jmaa.1995.1384C. V. Pao, Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions. J. Math. Anal. Appl. 195 (1995), No. 3, 702–718. 10.1080/00036819208840101E. Obolashvili, Nonlocal problems for some partial differential equations. Appl. Anal. 45 (1992), No. 1-4, 269–280. A. V. Bitsadze and A. A. Samarskii, On some simple generalizations of linear elliptic boundary problems. (Russian) Dokl. Akad. Nauk SSSR 185 (1969), 739-740; English transl.: Sov. Math., Dokl. 10 (1969), 398–400. D. G. Gordeziani, On the methods of solution of one class of nonlocal boundary value problems. Tbilisi State University Press, Tbilisi, 1986. D. V. Kapanadze, On a n onlocal Bitsadze-Samarski boundary value problem. (Russian) Differentsial’nye Uravneniya 23 (1987), No. 3, 543–545, 552. 10.1007/s10958-015-2317-5D. Devadze, V. Beridze. A Control Optimal Problem for Helmholtz Equations with Bitsadze–Samarski Boundary Conditions. Proceedings of A. Razmadze Mathematical Institute. 2013. Vol. 161. pp. 47-53. 10.1070/rm2013v068n04abeh004854D. Sh. Devadze and V. Sh. Beridze, Optimality conditions for quasilinear differential equations with nonlocal boundary conditions. UMN 68 (2013), No. 4. pp 179-180. 10.1070/im1972v006n03abeh001894V. I. Plotnikov, Necessary and sufficient conditions for optimality and conditions for uniqueness of the optimizing functions for control systems of general form. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 652–679. G. Berikelashvili. On the Solvability of a Nonlocal Boundary Value Problem in the Weighted Sobolev Spaces. Proceedings of A. Razmadze Mathematical Institute 119 (1999), 3-11 G. V. Meladze, T. S. Tsutsunava, and D. Sh. Devadze, An optimal control problem for quasi-linear differential equations of first order on the plane with nonlocan boundary conditions. Tbilisi State University Press, Tbilisi, 1987, deposited at the Georgian Institute of Technical and Scientific Information, 25.12.87, No. 372, Г87, 61 p. O. A. Ladizhenskaya and N. N. Uraltseva, Linear and quasilinear equations of elliptic type. (Russian) Nauka, Moscow, 1973. V. S. Vladimirov, The equations of mathematical physics. (Russian) Fourth edition. “Nauka”, Moscow, 1981. S. L. Sobolev, The Equations of Mathematical Physics. (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow– Leningrad, 1950. D. V. Kiryanov, Mathcad 14. BHV-Petersburg, St. Petersburg, 2007. M. Herhager and J. Partoll, Mathcad 2000: The Complete Guide: Trans. with Ger.-K. Publishing Group, BHV, 2000.