Sergey I. Kabanikhin

Fields of Research:

• Inverse problems of geophysics, acoustics, ecology, and medicine; 
• Ill-posed and inverse problems for differential and integral equations;
• Theory and numerical methods for solving inverse and ill-posed problems.

Research interests:

• numerical methods for solving inverse and ill-posed problems;
• geophysics, including seismics, electrical prospecting, gravity prospecting, and magnetic prospecting;
• tomography;
• processing of physical measurements, interpretation of data.

Major books:

1. Kabanikhin S. I. Projection-Difference Methods for Determining Coefficients of Hyperbolic Equations, Nauka, Novosibirsk, 1989.
2. Romanov V. G. and Kabanikhin S. I., Inverse Problems of Geoelectrics, Nauka, Moscow, 1991.
3. Romanov V. G. and Kabanikhin S. I. Inverse Problems for Maxwell’s Equations, Utrecht, The Netherlands, VSP, 1994, 249 p.
4. Kabanikhin S. I. and Lorenzi A. Identification Problems for Wave Phenomena, Utrecht, the Netherlands, VSP, 1999, 342 p.
5. Kabanikhin S. I., Satybaev A. D., Shishlenin M. A. Direct methods of solving inverse hyperbolic problems. 2004. VSP/BRILL, the Netherlands. 179 p.
6. Kabanikhin S. I. Inverse and Ill-Posed Problems. Sibirskoe Nauchnoye Izdatel’stvo, Novosibirsk, 2008, 450 p.
7. Kabanikhin S. I. Inverse and Ill-Posed Problems. Theory and Applications. De Gruyter, Germany, 2011, 459 p.

Current positions:

• Chairman, Academic Council, ICM&MG SB RAS;
• Member, Academic Councils, Sobolev Institute of Mathematics SB RAS and Mechanics and Mathematics Department of Novosibirsk State University;
• Chairman, Dissertation Council, ICM&MG SB RAS;
• Member, Bureau, RAS Department of Mathematical Sciences;
• Member, Presidium of SB RAS;
• Co-chairman, Program Committee of the annual international school-conference for young scientists “Theory and Numerical Methods of Solving Inverse and Ill-Posed Problems”, Novosibirsk, 2009-2018;
• Co-chairman, Program Committee of the international school-conference "Inverse Problems: Modeling and Simulation", Turkey, 2004, 2006, 2008, 2010, 2012, 2014, 2016;
• Editor–in-Chief, international series of books "Inverse and Ill-Posed Problems";
• Editor–in-Chief, international journal "Inverse and Ill-Posed Problems"  (Web of Science and Scopus);
• Editor–in-Chief, journal “Numerical Analysis and Applications" (Web of Science and Scopus);
• Member, Editorial Boards of journals “Open Applied Mathematics Journal", “Numerical Functional Analysis and Optimization”, “Siberian Journal of Industrial Mathematics”;
• Head, projects of the Russian Foundation for Basic Research;
• Academic Adviser of 19 Candidates of Science (later 8 of them defended their doctoral theses) and 4 Doctors of Science.

Major scientific results:

• development and justification of numerical methods for solving inverse problems of electrodynamics used in justifying a new method of electrical prospecting (RF patent 2062489) based on excitation and registration of unsteady electromagnetic fields;
• investigation of new inverse problems of geophysics, acoustics, electrodynamics, obtaining of theorems of uniqueness and stability of solutions;
• development and justification of new numerical algorithms for solving inverse problems of geophysics, acoustics, and electrodynamics; creation of corresponding software packages;
• investigation of optimization methods for solving inverse and ill-posed problems, obtaining of estimates of convergence rate;
• obtaining of estimates of strong convergence of gradient methods for solving inverse problems of acoustics, electrodynamics, and elasticity theory on the basis of estimates of conditional stability; this allowed introducing specific rules for terminating iterations depending on data errors;
• construction of multidimensional analogs of Gelfand-Levitan and Krein equations used to create a software package for numerically solving multidimensional inverse problems of acoustics and elasticity theory.

Teaching activities:

• 2017: teacher of mathematics, School of Physics and Mathematics, Novosibirsk;
• 1990 – present: Professor, Novosibirsk State University;
• 1978 – 1990: Associate Professor, Novosibirsk State University;
• 1977 – 1978: teacher of mathematics, School of Physics and Mathematics, Novosibirsk.

Scientific organization activities:

• Member of Specialized Dissertation Councils of the Institute of Mathematics, the Institute of Computational Mathematics and Mathematical Geophysics (ICM&MG), and the Institute of Geology and Geophysics of the Siberian Branch of the Russian Academy of Sciences (SB RAS);
• Member of the Councils of Experts, the Russian Foundation for Basic Research (RFBR) on Earth’s Sciences and Informatics;
• Chairman of the Council of Young Scientists, Siberian Branch of the USSR Academy of Sciences (1985-1988).

Scientific and teaching activities abroad (1984 – present):

• Vienna, Innsbruck, and Linz Universities (Austria);
• Oxford, Cambridge, and Bristol Universities (England);
• Institute of Mathematics of the Bulgarian Academy of Sciences (Bulgaria);
• Karlsruhe, Bayreuth, and Chemnitz Universities (Germany);
• Milan University; Florence University, and Institute of Global Analysis, Perugia University;
• Abai Kazakh National Pedagogical University, Al-Farabi Kazakh National University, Satbayev Kazakh National Technical University, Kazakh-British Technical University (Almaty, Kazakhstan);
• Vancouver University (Canada);
• Hangzhou, Beijing, Shanghai, Nanjing, and Tianjin Universities (China);
• University of North Carolina (Charlotte, USA);
• Ankara, Kocaeli, Izmit, and Fethiye Universities (Turkey);
• Institute of Geophysics (Prague, Bratislava, Czechoslovakia);
• Royal Institute of Technology (Stockholm, Sweden);
• Tokyo and Kyoto Universities (Japan).

19 PhDs and 8 Doctors of Science.

Author of 136 scientific publications including 8 books.

Major publications:

• Inverse and Ill-Posed Problems. Sibirskoe Nauchnoye Izdatel’stvo, Novosibirsk, 2009;
• Numerical regularization of multidimensional coefficient inverse problems. Abstracts of the International Conference «Marchuk Scientific Readings». Akademgorodok, Novosibirsk, Russia. June 25 – July 14, 2017;
• Numerical methods for solving inverse and ill-posed problems for elliptic and parabolic equations. Abstracts of the International Conference «Marchuk Scientific Readings». Akademgorodok, Novosibirsk, Russia. June 25 – July 14, 2017;
• Study of permittivity of borehole environment at the early stage of the formation process. Investigations of the Conditional ill-Posedness of Problems of Mathematical Physics. – Novosibirsk: Computing Center of the Siberian Branch of the USSR Academy of Sciences, 1989. pp. 40-59;
• Construction of a fundamental solution to a system of equations of elasticity theory. Siberian Electronic Mathematical Reports, Vol. 11, 2014;
• Singular decomposition in ill-posed problems. Textbook for institutes of higher education. Ust-Kamenogorsk, D. Serikbayev East Kazakhstan State Technical University, Novosibirsk State University, 2014;
• Algorithms and numerical methods for solving inverse and ill-posed problems. Monograph. Astana, 2012;
• Solution of the inverse problem of acoustics by the methods of Gelfand-Levitan and boundary control. Inverse Problems and Information Technologies, 2003. 2. No. 1;
• Inverse Problems of Geoelectrics, Moscow: Nauka, 1991. p.304;
• Finite difference regularization of a linearized inverse problem for a two-dimensional wave equation. Conditionally Well-Posed Problems.  Institute of Mathematics. Novosibirsk, Siberian Branch, USSR Academy of Sciences, 1987;
• Inverse Problems of Electrodynamics. Monograph. Novosibirsk, Computing Center, Siberian Branch, USSR Academy of Sciences, 1984;
• On one statement of a two-dimensional problem for the equation of oscillations. Ill-Posed Mathematical Problems and Geophysics Problems. Novosibirsk, Computing Center, Siberian Branch, USSR Academy of Sciences, 1976.