Books
1. Inverse Problems of Elecrodynamics, Novosibirsk, Computer Center, 1984 (joint with V. G. Romanov and T. P. Pukhnacheva, in Russian).
2. Projection-difference Methods for Determining of Hyperbolic Equations Coefficients, Nauka, Novosibirsk, 1988 (in Russian).
3. Inverse Problems of Geoelectrics, Moscow, Nauka, 1991 (joint with V. G. Romanov, in Russian).
4. Optimization Methods of Solving Inverse Hyperbolic Problems, Novosibirsk State University, 2002 (joint with K. T. Iskakov)
5. Inverse Problems for Maxwell’s Equations, Utrecht, The Netherlands, VSP, 1994 (joint with V. G. Romanov)
6. Identification Problems for Wave Phenomena, Utrecht, The Netherlands, VSP, 1999 (joint with A. Lorenzi)
7. Direct Methods of Solving Inverse Hyperbolic Problems, Utrecht, The Netherlands, VSP, 2004 (joint with M. A. Shishlenin and A. D. Satybaev)
8. Iterative Methods of Solving Inverse and Ill-Posed Problems with Data Given on the Part of the Boundary. Almaty-Novosibirsk, International Foundation: Inverse Problems, 2006 (joint with M. A. Bektemesov and A. T. Nurseitova, in Russian).Papers
- Kabanikhin S.I. On a formulation of the two-dimensional problems for an
oscillation equation. Incorrect Mathematical Problems and
Problems of Geophysics, Novosibirsk, 1976, pp. 64-73 (in Russian).- Kabanikhin S.I. Application of energy inequalities to an inverse problem
for a hyperbolic equation. Differential Equations, 1979,vol 15, pp. 61-67 (in Russian).- Kabanikhin S.I. The finite-difference method for determining the
coefficients of a hyperbolic equation. Zhurnal of Vychisl. Mat. i Mat. Fiziki.
1979, vol. 19, No 2, pp. 417-425 (in Russian).- Kabanikhin S.I., Romanov V.G. and Pukhnacheva T.P., On
the theory of Inverse problems of electrodynamics. Dokl. Akad.
Nauk SSSR, 1982 ,vol. 266, pp. 1070-1073.- Kabanikhin S.I. and Blagoveshensky A.S.,
Inverse problem of the theory of wave propagation in a semi-infinite
non-regular wavequide. Differential Equations, 1983 , vol. 19,
pp. 603-607 (in Russian).- Kabanikhin S.I.,
The solvability of inverse problems for differential equations.
Dokl. Akad. Nauk USSR,1984,vol. 277, pp. 788-791 (in Russian).- Kabanikhin S.I.,
Regularization of multidimensional inverse prlblems for hyperbolic
equation on the basis of a projection method.
Dokl. Akad. Nauk USSR, 1987, vol 292 , pp. 534-537 (in Russian).- Kabanikhin S.,I. and Bakanov G.B.,
Stability of a finite-difference analogue of a two-dimensional problem
of integral geometry. Dokl. Akad. Nauk SSSR, 1987, vol 292,1,
pp. 25-29 (in Russian).- Kabanikhin S.I.,
Linear regularization of multidimensional
inverse problems for hyperbolic equations. Dokl. Akad. Nauk SSSR
1989, vol. 309, 4 , pp. 791-795 (in Russian).- Kabanikhin S.I.,
Regularization of Volterra operator equations of the first kind with a
boundedly Lipschitz-continuous kernel.
Soviet Math. Dokl. 1989) ,vol . 39, 3 , pp. 549-552.
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Top- Kabanikhin S.I.,
On linear regularization of multi-dimentional inverse problems for
hyperbolic equations. Sov. Math. Dokl. 1990, vol 40, 3, pp. 579-583.- Kabanikhin S.I., Grasselli M. and Lorenzi A.,
An inverse hyperbolic integrodifferential problem arising in geophysics.
II. Nonlinear Anal. 1990, vol 15, 3 , pp. 283-298.- Kabanikhin S.I., Romanov V.G. and Bakanov G.B.,
Investigation of a differential-difference analogue of a three-dimensional
problem of integral geometry. Soviet Math. Dokl. 1990, vol. 41, 2, pp. 306-309.- Kabanikhin S.I. and Karchevsky A.L.,
Optimal control methods for solving the inverse problems of geoelectics.
Abstracts of XX General Assembly IUGG, 11-24 August, 1991, Vienna.- Kabanikhin S.I. and Iskakov K.T.,
The solution of one-dimensional inverse problem of geoelectrics
by the method of conjugate gradients. Russian Journal of
Theoretical and Applied Mechanics, 1991, vol. 3, 1991, USA, New York, pp. 78-88.- Kabanikhin S.I. and Lorenzi A.,
An Identification Problem Related to the Integrodifferential Maxwell's Equations.
Inverse Problems, 1991, vol. 7, pp. 863-886.- Kabanikhin S.I., Grasselli M. and Lorenzi A.,
An inverse problem for an integro-differential equation,
Siberian Mathematical Journal, 1992, vol. 33, 3 , pp. 415-426.- Kabanikhin S.I. and Karchevsky A.L.,
Optimization method of solving inverse problems of geoelectrics.
Ill-posed Problems in Natural Sciences, 1992, Ed. A. Tikhonov, VSP/TVP, The Netherlands,
pp. 312-325.- Kabanikhin S.I., Karchevsky A.L., and Lorenzi A.,
Regularization of Solutions to Linear Integrodifferential Inverse Problem.
Preprint 44, 1992, Universita di Milano, Dipartimento di Matimatica.- Kabanikhin S.I. and Romanov V.G.,
Inverse dynamic problems and numerical methods for solving them.
Ill-Posed Problems in Natural Sciences, 1992, Ed. A. Tikhonov, VSP/TVP,
The Netherlands.
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Convergence of finite-difference scheme inversion in problems of
determining the coefficients in hyperbolic equations.
Journal of Inverse and Ill-Posed Problems, 1993, vol 1, 1 , pp. 33-52.- Kabanikhin S.I. and Bimuratov S.Sh.,
Solution of a one-dimensional inverse problem of electrodynamics by the
Newton-Kantorovich method. Comput. Mathematics and Mathematical Physics.
1993, vol. 32, 12, pp. 1729-1743.- Kabanikhin S.I. and Bakanov G.B.,
On the stability estimation of finite-difference and differential-difference
analogues of a two-dimensional integral geometry problem.
Computirized Tomografy; Proceedings of the Fourth International
Symposium held in Novosibirsk (Russia) on 10-14 August, 1993,
Ed. M.M. Lavrent'ev, Utrecht: VSP, pp. 246-258.- Kabanikhin S.I., Karchevsky A.L. and Lorenzi A.,
Lavrent'ev's regularization of linear integrodifferential identification
problem. Conditionally well-posed problems of Mathematical
Phisics and Analysis, 1993, Ed. M.M.Lavrent'ev, VSP/TSP,
The Netherlands, pp. 343-346- Kabanikhin S.I., Karchevsky A.L., and Lorenzi A.,
Lavrent'ev's regularization of solutions to linear
integrodifferential inverse problem. Journal of
Inverse and Ill-posed Problems, 1993, vol 2 , VSP, The Netherlands,
pp. 115-141.- Kabanikhin S.I. and Romanov V.G.,
Inverse dynamic problems and numerical methods for solving them.
Conditionally Well-Posed Problems and Applications.
Proceedings of the Novosibirsk Conference, June
1993, Utrecht, VSP and TVP, pp. 227-266.- Kabanikhin S.I., Romanov V.G., Stroem S., He S.,
Analysis of the Green's function approach to
one-dimensional inverse problems. (I. One parameter reconstruction),
Journal of Mathematical Physics. 1993, vol. 34, 12,
pp. 5724-5746.- Kabanikhin S.I.,
Numerical Analysis of Inverse Problems. Abstracts of Inverse
Problem in Engineering Sciences, Osaka, July 27-30, 1994, pp. 15-16.- Kabanikhin S.I. and He S.,
An optimization approach to a three-dimensional acoustic inverse problem
in the time domain. TRITA-TET , vol. 94-98, Department of
Electromagnetic Theory, Royal Institute of Technology, Sweden, 1994.- Kabanikhin S.I. and Romanov V.G.,
Inverse Problems for Maxwell's Equations. Utrecht,
VSP, 1994, 240 pp.
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Numerical analysis of inverse problems.
Journal of Inverse and Ill-Posed Problems, 1995, vol. 3, 4. Pp. 278-304.- Kabanikhin S.I.,
Numerical algorithms for inverse problems. Abstracts of Advanced
Mathematics, Computations and Applications, Novosibirsk,
June 20-24, 1995, NCC Publisher, Novosibirsk, pp. 144-145.- Kabanikhin S.I. and Bakanov G.B.,
On the stability estimates of finite-difference and
differential-difference analogous of a two-dimensional
integral geometry problem. Computerized Tomography - 93,
The Netherlands, VSP, 1995, pp. 246-258.- Kabanikhin S.I. and Bakanov G.B.,
Gel'fand-Levitan approach to the discrete
inverse problem. Abstracts of Advanced Mathematics,
Computations and Applications, Novosibirsk, June 20-24, 1995,
NCC Publisher, Novosibirsk, pp. 145-146.- Kabanikhin S.I. and Gryazina G.Yu.,
Penalty method with internal prox-regularization for an inverse
source problem. Computerized Tomography - 93, The Netherlands, VSP,
1995 pp. 194-200.- Kabanikhin S.I. and Gryazina G.Yu.,
Penalty method with internal prox-regularization for an inverse source
problem. Abstracts of Advanced Mathematics,
Computations and Applications, Novosibirsk, June 20 -24, 1995,
NCC Publisher, Novosibirsk, pp. 145-146.- Kabanikhin S.,I. and He S.,
An optimization approach to a three-dimensional
acoustic inverse problem in the time domain.
Journal of Mathematical Physics. 1995, vol. 36, 8 , pp. 4028-4043.- Kabanikhin S.I. and Karchevsky A.L.,
Optimization method for solving the Cauchy problem for an elliptic
equation. Journal of Inverse and Ill-Posed Problems, 1995, vol. 3, 1,
pp. 21-46.- Kabanikhin S.I. and Karchevsky A.L.,
Optimal control in the cauchy problem for elliptic and parabolic
equations. Abstracts of Advanced Mathematics, Computations and
Applications, Novosibirsk, June 20-24, 1995, NCC Publisher, Novosibirsk,
p.146.- Kabanikhin S.I.,
Discrete inverse problems for hyperbolic equations. Abstracts .
Inverse and ill-posed problems. International conference dedicated to
the memory of academician A.N.Tikhonov, (IIPP-96). Moscow, Dialog-MSU,
1996, p.87.- Kabanikhin S.I. and Bakanov G.B.,
The optimizational method for solving the discrete inverse problem
for hyperbolic equation. Journal of Inverse and Ill-Posed Problems,
1996, vol. 4, 6 , The Netherlands, Utrecht, pp. 513-530.- Kabanikhin S.I. and Bakanov G.B.,
Discrete analogy of the Gelfand-Levitan equation.
Journal of Inverse and Ill-Posed Problems, 1996, vol. 4, 5,
pp. 409-435.- Kabanikhin S.I. and Bakanov G.B.,
Properties of the cost function in the hyperbolic
inverse problems. Abstracts. Inverse and ill-posed problems.
International conference dedicated to the memory of academician
A.N.Tikhonov, (IIPP-96) , Moscow, Dialog-MSU, 1996, p.24.- Kabanikhin S.I., Romanov V.G., Gottlieb J., Martakov S.V. and Schlaeger S.,
Identification of electromagnetic parameters for media with
microstructure. Abstracts of Conference on Inverse Problems of Wave
Propagation and Diffraction (September 23-27,1996), Aix-les-bains,
France, 1996, pp. 18-21.- Kabanikhin S.I. and Yamamoto M.,
The Gel'fand-Levitan theory for systems and its application
to nonstationary problems. Abstracts. Inverse and ill-posed problems.
International conference dedicated to the memory of academician
A.N.Tikhonov, (IIPP-96), Moscow, Dialog-MSU, 1996, p.87.- Kabanikhin S.I., Romanov V.G., Gottlieb J. and Martakov S.V.,
An inverse problem for special dispersive media arising from ground
penetrating radar. Journal of Inverse and Ill-Posed Problems, 1997,
vol. 5, 2, The Netherlands, Utrecht, pp. 175-192.- Kabanikhin S.I.,
Discrete inverse problems for hyperbolic equations.
2-nd Saxon Symposium on Inverse Problems,
Germany, Oybin, September 24-26, 1997.- Alekseenko A.,M., and Kabanikhin S.I.,
Uniqueness of the stationary point for the one-dimensional inverse problem
in two-dimensional space. Journal of Inverse and Ill-Posed Problems
1998 vol. 6(2), The Netherlands, Utrecht, pp. 95--114.- Alekseenko A.M., and Kabanikhin S.I.,
Identification of an electromagnetic source in Magnetoencephalography.
Journal of Inverse and Ill-Posed Problems (1998)
vol. 7(5), The Netherlands, Utrecht, pp. 95--114.- Kabanikhin S.I., Kowar R., and Scherzer O.,
On the Landweber iteration for the solution of a parameter identification
problem in the hyperbolic partial differential equation of the second
order. Journal of Inverse and Ill-Posed Problems (1998) vol.6(5),
The Netherlands, Utrecht, pp. 403--430.- Kabanikhin S.I., Koptyug I.,V., Iskakov K.T., and Sagdeev R.Z.,
Inverse problem for a quasilinear equation of diffusion.
Journal of Inverse and Ill-Posed Problems (1998) vol.6(4),
The Netherlands, Utrecht, pp. 335--352.- Kabanikhin S.I., Karchevsky A.L.,
Optimization algorithm of solving Cauchy problem for elleptic equation.
Dokladi Rossiiskoi Akademii Nauk (1998) vol.359(4), pp. 445--447- Kabanikhin S.I., Romanov V.G.,
Direct and inverse problems of electromagnetoelasticity.
Physics and Chemistry of the Earth (1998) vol.23(9/10), pp. 883--894.- Kabanikhin S.I., and Lorenzi A.,
Identification Problems of Wave Phenomena, Uthecht, The Netherlands,
VSP, (1999), 310pp.- Azamatov J.S., and Kabanikhin S.I.,
Nonlinear Volterra operator equations. L2 - theory.
Journal of Inverse and Ill-Posed Problems (1999)
vol.7(6), The Netherlands, Utrecht, pp. 487--510.- Alekseenko A.M., and Kabanikhin S.I.,
Numerical algorithm for identification problem of magnetoencephalography.
Journal of Inverse and Ill-Posed Problems (1999)
vol.7(5), The Netherlands, Utrecht, pp. 385--408.- Kabanikhin S.I.,
Numerical methods for solving acoustic inverse problem.
1-st Workshop on Inverse Problems in Underwater Acoustics,
Heraklion, Crete, HELLAS, May 17-19, 1999, p. 63.- Kabanikhin S.I.,
Numerical analysis of hyperbolic inverse problems in L2.
Inverse and Direct Problems and Applications,
Milano -- Gargnano, Italy, April 26-30, 1999.- Koptyug I.V., Kabanikhin S.I., Iskakov K.T., Fenelonov V.B.,
Khitrina L.Yu., Sagdeev R.Z. and Parmon V.N. A quantitative NMR
imaging studi of mass transport in porous solids during drying
Chemical Engineering Science, Pergamon v.55, 2000. pp.1559-1571.- Kabanikhin S.I., Koptyug I.V., Iskakov K.T. Inverse problem for the
diffusion equation and its application to describe the sorption process.
Tokyo, Japan. 2000- Kabanikhin S.I., Koptyug I.V., Iskakov K.T., Sagdeev R.Z. Inverse
problem for diffusion transport of water upon single pellet moisture sorbtion.
International Journal of Nonlinear Sciences and Numerical Simulation
Shanghai Universitet v.1, 2000, pp.31-42.- S.I. Kabanikhin, K.T. Iskakov and
M. Yamamoto, H1- conditional stability with explicit Lipshitz
constant for a one-dimensional inverse acoustic problem.
University of Tokyo, Graduate school of mathematical sciences,
Tokyo, Japan. (to appear)
