Laboratory of Theory of Inverse Problems |

The laboratory was established in 1976. The first head of the laboratory was Ph.D. M. Juraev, then during 10 years the laboratory was headed by a corresponding member of the Academy of Sciences of the Kyrgyz SSR A.I. Botashev, from 1996 to 2018 was by the Doctor of Physical and Mathematical Sciences, Professor A. Asanov, currently the laboratory is headed by Doctor of Physical and Mathematical Sciences Z.A.Kadenova. The formation of the laboratory and its further success were due to a close relationship with the Novosibirsk scientific school, where the laboratory staff had scientific internships (M. Juraev, E. R. Atamanov, A. A. Asanov, A. Sh. Mamausupov, B. R. Tabaldyev, A.A. Satybaev). Research in the laboratory was conducted in several directions: integral equations of the first kind, integral and operator Volterra equations of the first and third kinds, as well as problems of integral geometry (tomography) (A.Asanov, A.A. Srazhidinov and their disciples).Non-classical and inverse problems for partial differential equations were investigated by M. Juraev, E.R. Atamanov, A. Asanov, O.Sh. Mamayusupov, K.R. Tabaldyev, B.A. Ablabekov and their disciples. Numerical methods for solving inverse problems were investigated by A.S. Satybaev. Studies of these two areas are summarized in five monographs, four of which were published in Japan and Netherlands. A.I. Botashev was the author of a new method in the problem of multidimensional branching. These results are presented in his monograph. D.Sc. A.T. Alymbaev obtained a series of results on numerical, numerical-analytical, and asymptotic methods for studying boundary value problems. T.Sydykov and K. Belekov obtained the results on asymptotic methods for the study of nonlinear DE. A.M. Abdukarimov explores DE and IDE of partial derivatives in unbounded domains. The laboratory successfully works in the training of scientific workers and teachers for universities of Kyrgyzstan. Under the leadership of Professor A.Asanov 2 doctoral and 7 Ph.D. theses were defended. D.Sc. Z.A. Kadenova studies linear integral equations of the first kind with two independent variables in different domains. In addition, laboratory staff is involved in the preparation of textbooks in mathematics for schools and universities of our republic. Two textbooks on algebra in the Kyrgyz language for grade 9 and grade 11 have been published (M.I. Imanaliev, A.Asanov, S.Iskandarov, K.Zhusupov). A.Asanov has published 7 textbooks for universities of Kyrgyzstan. The steady growth of science and technology leads to the need to study new classes of equations relating to incorrectly posed problems. The efforts of the laboratory staff will be directed towards solving these problems. |