Galkin V.A. is a specialist in the field of nonlinear equations of physical kinetics and hydrodynamics, the author of 141 scientific papers, including 3 monographs.

The main scientific results of V.A. Galkin: in the field of nonlinear equations, it is computational stability, global convergence of approximations for systems of conservation laws related to physical kinetics and gas dynamics. These studies turned out to be naturally related to the problems for nonlinear systems of conservation laws, including the equations of gas dynamics, hydrodynamics, Korteweg-de-Vries, Kadomtsev-Petviashvili, Maxwell-Vlasov-Liouville systems, etc. Fundamental results were obtained on finding out correctness classes, development and justification of global convergence of approximate methods for nonlinear conservation laws in the space of functional solutions, endowed with A.N. Tikhonov topology, introduced by V.A. Galkin. These results of V.A. Galkin have been widely discussed by the international scientific community over the past 30 years, they are recognized and constantly supported by grants from the RFBR, INTAS (000679), ISTC (2992, 2005).

Galkin V.A. conducts educational work: he trained about 125 graduate students, under his supervision 12 PhD students received a PhD degree, one of whom defended his doctoral dissertation at the INS RAS in the field of science developed by V.A. Galkin for 40 years. In 1993 V.A. Galkin was awarded the diploma of the Committee on Higher Education of the Russian Federation «for supervising a thesis awarded with a medal in the All-Russian Competition in the Natural Sciences».

 Galkin V.A. conducts significant work related to the organization and holding of international conferences. The international conferences organized by V.A. Galkin: «Mathematical Physics, Mathematical Modeling and Approximate Methods», dedicated to Academician A.N. Tikhonov (Obninsk, May 2000) and «Mathematical Ideas of P.L. Chebyshev and Their Applications to Contemporary Problems in Natural Sciences» (Obninsk, May 2002, November 2004, May 2006, May 2008, May 2011). Two international conferences «Mathematics and Information Technologies in the Oil and Gas Complex» were held in Surgut in 2014 and 2016 with the support of the RFBR. Together with academician N.S. Bakhvalov and prof. Yu.A. Dubinsky he took part in the RFBR project to perpetuate the memory of a prominent Russian scientist and mathematician S.N. Kruzhkov (compilation and preparation to publication of the book «The Works of S.N. Kruzhkov», M.: FIZMATLIT, 2000, 336 P.). Since 2015 to 2019, he has been Vice Chief Editor of the electronic journal "Proceedings in Cybernetics", and since 2020 – Vice Chief Editor of the electronic journal "Russian Journal of Cybernetics".

V.A. Galkin was Head of the Department of Applied Mathematics of the Obninsk Institute for Nuclear Power Engineering from 1999 to 2012. 

From 2010 to 2012 Galkin V.A. was Head of the Obninsk Institute for Nuclear Power Engineering, a branch of the National Research Nuclear University MEPhI, from 2013 to 2018 he was Director of the Polytechnic Institute of the Surgut State University (SurSU). From 2006 he was a professor and Head of the Department of Informatics and Computing Techniques at SurSU. Then from 2007 he was a professor and Head of the Department of Applied Mathematics at SurSU. He was elected professor of this department in June 2018.

In 2016 Galkin V.A. was nominated as a Corresponding Member of the RAS in the Department of Mathematical Sciences of the RAS with a degree in Applied Mathematics and Informatics by the Academic Council of the Federal State Institution «Federal Research Center Scientific Research Institute of System Analysis  of the Russian Academy of Sciences».

He is an Honorary Worker of Higher Professional Education of the Russian Federation since 2002 and has 42 years of experience in research and teaching activities.

In 2016 he was awarded the Kh. A. Rakhmatulin medal for a major contribution to the development of computational methods in solving problems of mechanics by the Russian National Committee on Theoretical and Applied Mechanics.

Since 1996 he organizes international conferences in Obninsk and Surgut, dedicated to the memory of the great mathematician and member of the Russian Academy of Sciences P. L. Chebyshev. 

Since November 2018 professor V.A. Galkin is Head of the Separate Department of the Federal State Institution «Federal Research Center Scientific Research Institute of System Analysis of the Russian Academy of Sciences» in Surgut.

Major Publications

In Russian

1. Galkin V. A., Dubovik A. O. On one class of exact solutions of the Navie–Stokes system of equations for an incompressible fluid // Matem. Mod. 2023. Vol. 35. No. 8. P. 3–13.
2. Galkin V.A., Smorodinov A.D., Morgun D.A. Solution of the Navier–Stokes Equation for Colliding Jets // Russian Journal of Cybernetics. 2023. Vol. 4, № 2. P. 8-15.
3. Galkin V. A. On a class of exact solutions to the incompressible Navier–Stokes system in a ball and a spherical layer // Comput. Math. Math. Phys. 2023. Vol. 63. No. 6. P. 1064–1069.
4. Betelin V. B., Galkin V. A. On Fixed Points of Continuous Mappings Associated with Construction of Artificial Neural Networks // Dokl. Math. 2022. Vol. 106. P. 423–425.
5. V.B.Betelin, V.A.Galkin. On the Formation of Structures in Nonlinear Problems of Physical Kinetics// Doklady Mathematics, 2019, Vol. 99, №1
6. Galkin V. A., The smoluchowski equation of the coagulation   theory: spatially uniform systems: monograph / V.A. Galkin; Surgut State University.  – Kurgan: ООО  «Курганский Дом печати», 2016. – 228 p. ISBN 978-5-89545-445-9.
7. Galkin V. A., Dubovik А. О., Yepifanov А. А. Approximate Methods for Solving Incompressible liquid Equations // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki (Computational Mathematics and Mathematical Physics). 2017. Vol. 57, No. 2.  P. 105–114.
8. Betelin V. B., Yeskov V. М., Galkin V. А., Gavrilenko Т. V. Stochastic Instability of Complex Homeostatic System Dynamic Behavior // Doklady Mathematics, 2017, Vol. 472 ,№1, pp. 642–644.
9. Betelin V. B., Galkin V. A., Dubovik A. O.  On Controllable Viscous Incompressible Fluid Flow As Applied to a Magnetic Hydrodynamics Model // Doklady. Mathematical Physics. 2016. Vol. 470, No. 2. P. 150-152.
10. Betelin V. B., Galkin V. A. Incompressible Fluid Parameters Control as the Flow Geometry Changes Over Time // Academy of Sciences Proceedings. 2015. Vol. 463. No. 2. P. 149-151.             
11. Betelin V. B., Galkin V. A., Gorelikov A. V. A Predictor-Corrector Algorithm for a Numerical Solution of the Induction Equation for MHD Viscous Incompressible Fluid Analysis // Academy of Sciences Proceedings. 2015. Vol. 464. No. 5. P. 525-528.
12. Galkin V. A., Bychin I. V., Skryleva E. A., Gavrilenko T. V., Galkina I. V., Galkin A. V., Gorelikov A. V., Egorov A. A., Epifanov A. A., Morgun D. A., Nazin A. G., Ryakhovsky A. V. Phase Separation Modeling and Control in Poorly Compressible Viscous Heat Conductive Oil-like Liquids with Gaseous and Solid Inclusions // Proceedings in Cybernetics. 2015. No. 3 (19). P. 21-37.
13. Galkin V. A., Gorelikov A. V., Gavrilenko T. V., Ryakhovsky A. V., Bychin I. V. A Software Package for Simulating Convection in Spherical Layers Running on Hybrid Computing Systems (CPU/GPU) // Mathematical Modeling. 2014. Vol. 26. No. 10. P. 95-108.
14. Galkin V. A. A Kinetic Approach to Solving Differential Equation Systems// Academy of Sciences Proceedings. 2013. Vol. 452. No. 1. P. 12-13.
15. Galkin V. A. Generalized Solutions of a Semilinear Smoluchowski Equations System, and Their Approximations // Academy of Sciences Proceedings. 2012. Vol. 443. No. 3. P. 283-285.
16. Galkin V. A., Galkin A. V., Zdorovtsev P. А., Osetsky D. Yu. A Computational Model of Spatially Heterogeneous Slow Coagulation // Journal of Computational Mathematics and Mathematical Physics. 2012. No. 11. P. 2101-2012.
17. Galkin V. A. A Metric Theory of the Functional Solutions to the Cauchy Problem for Conservation Law Systems // Academy of Sciences Proceedings. 2010. Vol. 431. No. 3. P. 298-300.
18. Galkin V. A. Mathematical Models Analysis: Conservation Law Systems, Smoluchowski and Boltzmann Equations Moscow : BINOM, 2009. 408 p.
19. Galkin V. A., Saveliev V. I. Low Temperature Plasma Encyclopedia (Series B, Vol. VII-1 Low Temperature Plasma Mathematical Modeling. Chapter 6. Mathematical Modeling of Transient Radiation in Media with Quick-Changing Electromagnetic Properties Pp. 348-364 (Part III). Moscow : Janus-K Publishing, 2009.
20. Galkin V. А., Osetsky D. Yu. Mathematical Modeling of Coagulation Kinetics // Mathematical Modeling. 2006. No. 1. P. 99-117.
21. Galkin V. А., Osetsky D. Yu. A Case of Boltzmann Gas Leading to Smoluchowski Coagulation Equation // Journal of Computational Mathematics and Mathematical Physics. 2006. No. 3. P. 535-547.
22. Galkin V. А., Zabudko M. A., Osetsky D. Yu., Ryzhikov D. A., Galkina I. V. Mathematical Modeling of Agglomerate Growth Process with Smoluchowski and Vlasov-Liouville-Smoluchowski Approximations // Nizhny Novgorod Lobachevsky University Proceedings . Mathematical Modeling and Optimal Control Series, Vol. 1 (28) 2005. P. 67-74.
23. Galkin V. A. Convergence of Difference Schemes and the Direct Modeling Method to Smoluchowski Equation Solutions in the Kinetic Coagulation Theory // Russian Academy of Sciences Proceedings. 2004. Vol. 497. No. 1. P. 4-11.
24. Galkin V. А., Ryzhikov D. A., Saveliev V. I. Emitted Spectrum of Charged Particles Traveling in Heterogeneous Medium // Nuclear Energy. 2004. No. 2. P. 118-125.
25. Galkin V. А. The Smoluchowski Equation. Moscow : PHYSMATLIT, 2001. 336 p.
26. Galkin V. А., Zabudko M. А. Analytical and Numerical Solutions of Nonlinear Heat Conductivity Equations and Kinetic Equations // Mathematical Modeling. 2001. Vol. 13. No. 12. P. 46-54.
27. Galkin V.A. A Theory of Functional Conservation Law Solutions and Its Applications // I.G. Petrovsky Seminar Proceedings Vol. 20. Moscow, MSU University Press, 2000. P. 81-120.
28. Galkin V.А., Zabudko M, А. Exact and Numerical Solutions of the Heat Conductivity Equation and Kinetic Equations // University Proceedings. Nuclear Energy. 2000. No. 1. P. 19-28.
29. Galkin V. А., Tkachenko M. G. Numerical Solution of Vlasov Equations Used for NPP Modeling// University Proceedings. Nuclear Energy. 1999. No. 1. P. 94-103.
30. Galkin V. A., Badasarova I. Р. Periodical Structure Modeling for Determining Distribution of Defects in NPP Materials Exposed to Permanent Radiation Source // University Proceedings. Nuclear Energy. 1999. No. 1. P. 85-93.
31. Galkin V. A., Badasarova I. Р. Spatially Uniform Coagulation Modeling // Mathematical Modeling. 1999. Vol. 11. No. 6. 82-112.
32. Galkin V. A. Selecting Global Correctness Classes for Functional Solutions to Conservation Law Systems // Basic and Applied Mathematics. 1998. Vol. 4, No. 8. P. 853-868.
33. Galkin V. A. Approximation Methods Applicability to Conservation Law Systems // Moscow State University Proceedings Series 1, Mathematics and Mechanics 1995. No. 6. P. 55-59.
34. Galkin V. A. Russkikh V.V. Approximation Methods Convergence for Incompressible Fluid Equations // Mathematical Modeling 1994. No. 3. Р. 101-113.
35. Galkin V. A. A Functional Solutions of the Conservation Laws // USSR Academy of Sciences Proceedings 1990. Vol. 310. No. 4, P. 834-839.
36. Galkin V. A., Tupchiev V. A. On Average Solvability of a Quazilinear Conservation Laws System // USSR Academy of Sciences Proceedings 1988. Vol. 300. No. 6, P. 1300-1304.
37. Galkin V. A. A On Solving Physical Kinetics Equations // USSR Academy of Sciences Proceedings 1988. Vol. 298. No. 6. P. 1362-1367.
38. Galkin V.A. A Generalized Smoluchowski Kinetic Equation Solution for Spatially Heterogeneous Systems // USSR Academy of Sciences Proceedings 1987. Vol. 293. No. 1. P. 74-77.
39. Galkin V. A., Dubovskii P. B. A On Solving Coagulation Equations with Unlimited Cores // USSR Academy of Sciences Proceedings 1986. Vol. 22. No. 3. P. 504-509.
40. Galkin V. A. On the Smoluchowski Kinetic Coagulation Theory Equation for Spatially Heterogeneous Systems // USSR Academy of Sciences Proceedings 1985. No. 5. P. 1087-1091.
41. Galkin V. A. On Solving the Kinetic Coagulation Equation with Ф=xy Core // Metrology and Hydrology. 1984. No. 5. P. 33-39.
42. Galkin V. A. On an Atmospheric Aerosol Coagulation Feature // Metrology and Hydrology. 1983. No. 12. P. 11-19.
43. Galkin V. A., Burobin A.V. On Coagulation Equation Solutions // Differential Equations. 1981. Vol. 17. No. 4. 669-677.
44. Galkin V. A. An Iterative Solution Method for a Class of Evolution Equations Applied to Physical Kinetics // Journal of Computational Mathematics and Mathematical Physics 1981. Vol. 21. No. 2. P. 385-399.
45. Galkin V. A., Tupchiev V. A. On an Asymptotic Behavior of a Coagulation Equation Solution // Experimental Meteorology Institute Proceedings. Moscow : Hydrometizdat, Vol. 19. 1978. P. 31-39.
46. Galkin V. A., On the Stability and Stabilization of a Coagulation Equation Solution // Differential Equations. 1978. Vol. 14. No. 10. P. 1869-1874.
47. Galkin V. A., On the Existence and Uniqueness of a Coagulation Equation Solution // Differential Equations. 1977. Vol. 13. No. 8. P. 1460-1470.

In English

1. Galkin V. A., Dubovik A. O., Epifanov A. A. Approximate Methods for Equations of Incompressible Fluid // Computational Mathematics and Mathematical Physics. 2017. Vol. 57, No. 2. P. 272–280. 
2. Betelin V. B., Eskov V. M., Galkin V. A., Gavrilenko T. V. Stochastic Volatility in the Dynamics of Complex Homeostatic Systems // Doklady Mathematics, 2017, Vol. 95 ,№1, pp. 92-94.
3. Betelin V. B. , Galkin V. A., Dubovik A. O. On the Control of Layered Flow of a Viscous Incompressible Fluid within MHD //  Doklady Mathematics. 2016. Vol. 94, No. 2. P. 591–593. 
4. Betelin V. B., Galkin V. A. Control of Incompressible Fluid Parameters in the Case of Time-Varying Flow Geometry // Doklady Mathematics, Pleiades Publishing, 2015. Vol. 92. No. 1, pp. 511-513.
5. Betelin V. B., Galkin V. A., Gorelikov A. V. Predictor-Corrector Algorithm for the Numerical Solution of the Magnetic Field Equation in Viscous Incompressible MHD Problems // Doklady Mathematics, Pleiades Publishing. 2015. Vol. 92. No. 2. Р. 1-4.
6. Galkin V. A., Gorelikov A. V., Gavrilenko T. V., Ryakhovsky A. V., Bychin I. V Software for Numerical Simulation of Convection in Spherical Shells for Hybrid CPU/GPU Computing Systems // Mathematical Models and Computer Simulations, Pleiades Publishing. 2015. Vol. 7. No. 3. Р. 271-280.
7. Galkin V. A., Zdorovtsev P. A. Solutions of Momentum Chains for the Transport Equation and their Approximations // Mathematical Models and Computer Simulations, Pleiades Publishing, 2013. Vol. 5. No. 3. Р. 289-293.
8. Galkin V. A. Kinetic Method for Solving Systems of Differential Equations // Doklady Mathematics, Pleiades Publishing. 2013. Vol. 88. No. 2. Р. 508-509.
9. Galkin V. A. Generalized solutions of the Smoluchowski Semilinear System of Equations and Their Approximations // Doklady Mathematics, Pleiades Publishing. 2012. Vol. 85. No. 2. Р. 212-214.
10. Galkin V. A. Metric Theory of Functional Solutions of the Cauchy Problem for a System of Conservation Laws // Doklady Mathematics, Pleiades Publishing. 2010. Vol. 81. No. 2. Р. 219-221.
11. Galkin V. A. et al. The Detection of Neutrino Interactions in the Emulsion/Lead Target of the OPERA Experiment // Journal of Instrumentation. V. 4. No. 1. 2009.
12. Galkin V. A. et al. The OPERA experiment in the CERN to Gran Sasso Neutrino Beam // Journal of Instrumentation. 2009. V. 4. No. 1.
13. Galkin V. A. et al. Study of the Effects Induced by Lead on the Emulsion Films of the OPERA Experiment // Journal of Instrumentation. 2008. V.3. No. 1.
14. Galkin V. A. et al. Emulsion Sheet Doublets as Interface Trackers for the OPERA Experiment // Journal of Instrumentation. 2008. V. 3. No. 1.
15. Galkin V. A. Background of Mathematical Models, Based on Conservation Laws Systems // Industrial Mathematics. Narozsa Publishing House. New Delhi, India, 2006. Р. 159-178.
16. Galkin V. A. Singularities of the Solutions of the Infinite-Dimensional Hyperbolic Smoluchowski System, Describing Coagulation Process // Differential Equations, World Scientific Co, Singapore. 2005. Р. 505-511.
17. Galkin V. A. Background of Computations for Mathematical Models, Based on Conservation Laws Systems and Applications to Fluid dynamics. Parallel Computational Fluid Dynamics // Advanced Numerical Methods Software and Applications. Elsiver, 2003. Р. 357-366.
18. Galkin V. A. Global Correctness of Cauchy problem for Nonlinear Conservation Laws System and One Example for The Gas Dynamics. International Series of Numerical Mathematics. 1999. Vol. 129. P. 361-368. Birkhauser, Verlag Basel. Switzerland.
19. Galkin V. A. et al. Simulation and Optimization of the Heat Transfer Process for Single Crystal Growth in the Microgravity Conditions // European and NASA Conference on the Microgravity. St. Petersburg. 1997.
20. Galkin V. A., Russkikh V. V. On the Background of Limit Path for the Korteweg de Vries Equation as the Dispersion Vanishes // Acta Applicande Matematicae. 39. 1995. Р. 307-314. Kluwer Academic Publishers. Printed in Netherlands.
21. Galkin V. A. Nonlinear Boundary Value Problems and Simulation of Heat- Electricity Process // Fourth Int. Conf. on Simulation of Devices and Technologies, Univ. of Pretoria Ed. Printed in South Africa. 1995. P. 210-213.
22. Galkin V. A. Convergence and Numerical Stability of Approximate Methods for Conservation Laws // International Journal of Modern Physics C. 1994. Vol. 5. No. 2. Р. 207-214. 
23. Galkin V. A., Dubovskii P. B. , Stewart I. W. Exact Solution for the Coagulation-Fragmentation Equation // J. Physics A: Math. Gen., 1992. V. 25. 4737-4744.