Professor in Department of technical cybernetics
Research interests
- Differential Equations and Dynamical Systems;
- Singular Perturbations;
- Control Theory;
- Dynamics and Control Problems for Systems of Rigid Bodies and Particles;
- Gyroscopic and Robotic Systems;
- Geometrical Methods and Integral Manifolds Theory;
- Slow/Fast Models in Biomedical Systems;
- Mathematics of Combustion and Explosion and Chemical Kinetics.
Training of scientists
Ph.D Students Supervised:
Natalia Pendyukhova Voronezh State University 1989.
Georgiy Gorelov Voronezh State University 1992.
Elena Schepakina Samara State Pedagogical University 1995.
Elena Zharikova Samara State Pedagogical University 1995.
Evgenyi Abramochkin Samara State Pedagogical University 1996.
Sergey Ozersky Samara State Pedagogical University 1997.
Iliya Andreev Mordovia State University 1998.
Vladimir Sirochenko Samara State University 1999.
Dmitry Kurganov Samara State University 2003.
Oleg Rasskazov Yaroslavl State University 2004.
Elena Kitaeva Voronezh State Technological Institute 2005.
Ekaterina Schetinina Voronezh State University 2005.
Marina Semenova Yaroslavl State University 2006.
Olga Vidilina Voronezh State University 2007.
Elena Tropkina Voronezh State University 2013.
Michail Osintcev Samara State Aerospace University 2014.
Publications
1. Sobolev V.A. Canards and the effect of apparent disappearance // International Conference Information Technology and Nanotechnology, ITNT 2015, 28 июня - 1 июля 2015, Австрия, CEUR, Workshop Proceedings , 2015, P. 190-197
2. Korobeinikov A., Archibasov A., Sobolev V. Order reduction for an RNA virus evolution model // Mathematical Biosciences and Engineering. 2015. V. 12, Iss. 5. P. 1007-1016
3. Shchepakina E., Sobolev V., Korobeinikov A. Paradox of enrichment and system order reduction: bacteriophages dynamics as case study // Mathematical Medicine and Biology. 2015. 15. P. 1-13
4. Archibasov A.A., Korobeinikov A., Sobolev V.A. Asymptotic expansions of solutions in a singularly perturbed model of virus evolution // Computational Mathematics and Mathematical Physics. 2015. Volume 55, Issue 2. P. 240-250
5. Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell Singular Perturbations: Introduction to system order reduction methods with applications . Berlin: Springer, 2014. 212 С?.
6. Osintsev M.S., Sobolev V.A. Reduction of dimension of optimal estimation problems for dynamical systems with singular perturbations // Computational Mathematics and Mathematical Physics. 2014. Volume 54, Issue 1. P. 45-58
7. Sobolev V.A. Canard cascades // Discrete and Continuous Dynamical Systems. 2013. - Т.18. - ?2.. P. 513 - 521
8. Sobolev V.A., Osintsev M. Dimensionality reduction in optimal control and estimation problems for systems of solid bodies with low dissipation // Automation and Remote Control. 2013. - Т.74. - ?8.. P. 1334 - 1347
9. Sobolev V.A., Tropkina E.A. Asymptotic expansions of slow invariant manifolds and reduction of chemical kinetics models // Computational Mathematics and Mathematical Physics. 2012. - Т.52. - ?1.. P. 75-89
10. Sobolev V.A., Ointsev M.S. Slow integral manifolds in control and graduate education in Samara // IFAC Proceedings Volumes (IFAC-PapersOnline). 2012. - Т.9. - ?1.. P. 45 - 50
11. Sobolev V.A., Pokrovskii, A. and others. Topological degree in analysis of canard-type trajectories in 3-D systems // Applicable Analysis.. 2011. 90: 7.. P. 1123-1139
12. Sobolev V.A., Osintsev M. Global Invariant Manifolds in a Problem of Kalman Filtering for Gyroscopic Systems // Global and Stochastic Analysis.. 2011. Vol. 1, No. 1, June. P. 101-122
13. Sobolev V.A., Sazhin S.S., Shchepakina E.A. Order reduction of a non-Lipschitzian model of monodisperse spray ignition // Mathematical and Computer Modelling. 2010. 2010, vol. 52, issue 3-4. P. 529-537