On an inverse boundary-value problem for a second-order elliptic equation with non-classical boundary conditions

Yıl 2020, Cilt: 41 Sayı: 2, 443 - 455, 25.06.2020

Rauf Amirov Yaşar Mehraliyev Nergiz Heydarzade

https://doi.org/10.17776/csj.684366

Öz

An inverse boundary value problem for a second-order elliptic equation with periodic and integral condition is investigated. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, we perform a conversion from the original problem to some auxiliary inverse problem with trivial boundary conditions. By the contraction mapping principle we prove the existence and uniqueness of solutions of the auxiliary problem. Then we make a conversion to the stated problem again and, as a result, we obtain the solvability of the inverse problem.

Anahtar Kelimeler

inverse boundary value problem, elliptic equation, Fourier method, classical solution

Kaynakça

• [1] Tikhonov A.N., On stability of inverse problems, , [in Russian], Dokl. AN SSSR, 39(5) (1943) 195– 198..
• [2] Lavrent’ev M.M., On an inverse problem for a wave equation, [in Russian], Dokl. AN SSSR, 157(3) (1964) 520–521.
• [3] Lavrent’ev M.M. Romanov V.G. Shishatsky S.T., Ill-posed problems of mathematical physics and analysis, [in Russian], M., Nauka, 1980.
• [4] Ivanov V.K. Vasin V.V. Tanana V.P., Theory of linear ill-posed problems and its applications, [in Russian], M., Nauka, 1978.
• [5] Denisov A.M., Introduction to theory of inverse problems, , [in Russian], M. MGU, 1994.
• [6] Iskenderov A. D., The inverse problem of determining the coefficients of an eliptic equation, Journal of Differential Equations, 15(5) (1979) 858-867.
• [7] Aliyev R. A., On determining the coefficients of a linear elliptic equation, Sib. Journal of industry Mathematics, 19(2) (2016) 17-28
• [8] Solovyev V. V., Inverse problems for elliptic equations on a plane. Journal of Dif. Equations, 42(8) (2008) 1106-1114.
• [9] Megraliyev Y. T., The inverse boundary value problem for second- order elliptic equation with an additional integral condition, Bulletin of the Udmurt University, Mathematics, Mechanics, Computer Science, 1 (2012) 32-40.
• [10] Khudaverdiyev K. I. Veliyev A. A., The study of a one- dimensional mixed problem for one class of third-order pseudo-hyperbolic equations with nonlinear operator right- hand side, Baku: Chashiogly, 2010, 168P.