Inverse Problem of Determining the Unknown Coefficients in an Elliptic Equation

d2ee724b-c572-4b84-b343-a1d33991045520240515065040415wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511220241220242310.37394/23206.2024.23https://wseas.com/journals/mathematics/2024.phpInverse Problem of Determining the Unknown Coefficients in an Elliptic EquationBasti̇Ali̇yevaFaculty of Economics of Turkish World, Department of Economics and Business Administration, Azerbaijan State University of Economics (UNEC), Baku, Istiglaliyat str. 6, AZ1001, AZERBAIJANhttps://orcid.org/0000-0002-3274-5301The inverse problem of determining the coefficients of an elliptic equation under different boundary conditions in a given rectangle is considered. These problems lead to the necessity of approximate solution of inverse problems of mathematical physics, which are incorrect in the classical sense. The existence, uniqueness, and stability theorems for the solution of the set inverse problem are proved and a regularizing algorithm for determining the coefficient is constructed.51520245152024351358https://wseas.com/journals/mathematics/2024/a765106-1932.pdf10.37394/23206.2024.23.38https://wseas.com/journals/mathematics/2024/a765106-1932.pdf10.1201/9781482292985Prilepko A.I., Orlovsky D.G. Aleksey I., Igor A. Vasin. Methods for Solving Inverse Problems in Mathematical Physics, 732 Pages. Published March 21, 2000. Romanov V.G., İnvers problems of mathematical physics. VNU Science Press, Utrecht, the Netherlands, 1987. 10.1016/b978-0-12-804651-7.00015-8Aster, Richard C., Borchers, Brian, Thurber, Clifford H. Parameter Estimation and Inverse Problems, Elsevier, 3rd ed., 2019. Samarskii A. A., Numerical methods for solving inverse problems of mathematical physics, Walter de Gruyter, 2007. Kern, Michel, Numerical methods for inverse problems, Wiley-ISTE, 2016. 10.1007/s10958-019-04184-2Prilepko A.I., Kosten A.B.,Solovev V.V. Inverse source and coefficient problems for coefficient problems for elliptic and parabolic equations in Hoder and Sobolev spaces. Journal of Mathematical Sciences, Vol. 237, No. 4, March, 2019. 10.37394/23206.2023.22.35Aliyeva. B.M: The Inverse Problem of Determining the Coefficients Elliptic Equation, WSEAS Transactions on Mathematics, Vol. 22, 2023, 292-297, https://doi.org/10.37394/23206.2023.22.35. Farajov. A.S.: On a solvability of the nonlinear inverse boundary value problem for the boussinesq equation. Advanced Mathematical Models & Applications, 7(2), (2022) 241-248. 10.1007/s10958-023-06370-9Lyubanova, A.S., Velisevich, A.V. An Inverse Problm for a Quasilinear Elliptic Equation, JMath Sci 270, 591–599 (2023). 10.1007/s10598-020-09478-8Tuikina S.R. A numerical method for the solution of two inverse problems in the mathematical model of redox sorption (2020), Computational Mathematics and ode ling, Consultants Bureau (United States), vol. 31, № 1, 96-103, https://doi.org/10.1007/s10598-020-09478-8.