Sobolev, Vladimir A.

2024

• 1 Antonov D.V., Nizovtsev M.I., Shchepakina E.A. etc. Heat transfer through a three-layer wall considering the contribution of phase change: A novel approach to the modelling of the process // International Journal of Heat and Mass Transfer 2024. — Vol. 226.
• 2 Antonov D.V., Shchepakina E.A., Sobolev V.A. etc. A new solution to a weakly non-linear heat conduction equation in a spherical droplet: Basic idea and applications // International Journal of Heat and Mass Transfer 2024. — Vol. 219.
• 3 Antonov D.V., Strizhak P.A., Shchepakina E.A. etc. A COMBINED ANALYTICAL/NUMERICAL APPROACH TO THE MODELING OF THE PROCESSES LEADING TO PUFFING AND MICRO-EXPLOSION IN A COMPOSITE MULTI-COMPONENT FUEL/WATER DROPLET // Atomization and Sprays 2024. — Vol. 34. Issue 3. № 3. — P. 31-51
• 4 Zhang L., Wang J., Shchepakina E. etc. New solitary waves in a convecting fluid // Chaos, Solitons and Fractals 2024. — Vol. 183.
• 5 Sobolev V.A. Singularly Perturbed Optimal Tracking Problem // Differential Equations 2024. — Vol. 60. Issue 4. № 4. — P. 533-549

1991

• 1 Sobolev V.A. Geometrical theory of singularly perturbed control systems // IFAC Symposia Series - Proceedings of a Triennial World Congress. — 1991. — Vol. 3. — P. 415-420
• 2 Sobolev V.A. Singular perturbations in a linear-quadratic problem of optimal control // Avtomatika i Telemekhanika 1991. — Issue 2. — P. 53-64
• 3 Gorelov G.N., Sobolev V.A. Mathematical modeling of critical phenomena in thermal explosion theory // Combustion and Flame 1991. — Vol. 87. Issue 2. — P. 203-210

1998

• 1 Mironova V.A., Sobolev V.A., Tsyrlin A.M. Optimal control of the flows of raw materials and finished products by the price choice // Avtomatika i Telemekhanika 1998. — Issue 2. — P. 91-100
• 2 Voropaeva N.V., Sobolev V.A. Decomposition of singularly perturbed differential systems // Computational Mathematics and Modeling 1998. — Vol. 9. Issue 1. — P. 28-37

1997

• 1 Shchepakina E., Andreev I.A., Sobolev V. Modeling of Critical Phenomena in Autocatalytic Burning Problems // 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. — 1997. — P. 317-322
• 2 Zharikova EN, Sobolev, VA Optimal periodic systems of control with singular perturbations // Automation and Remote Control 1997. — Vol. 58. Issue 7. — P. 1188-1202

1996

• 1 Gol'dshtein V., Zlnoviev A., Sobolev V. etc. Criterion for thermal explosion with reactant consumption in a dusty gas // Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 1996. — Vol. 452. Issue 1952. — P. 2103-2119
• 2 Sobolev V.A., Shchepakina E.A. Duck trajectories in a problem of combustion theory // Differential Equations 1996. — Vol. 32. Issue 9. — P. 1177-1186
• 3 Gol'dshtein V., Sobolev V., Zinoviev A. Thermal explosion in a dusty gas // ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 1996. — Vol. 76. Issue SUPPL. 2. — P. 533-534

1995

• 1 Voropaeva NV, Sobolev, VA A constructive method of decomposition of singularly perturbed nonlinear differential systems // Differential Equations 1995. — Vol. 31. Issue 4. — P. 528-537

1994

• 1 Kononenko L.I., Sobolev V.A. Asymptotic decomposition of slow integral manifolds // Siberian Mathematical Journal 1994. — Vol. 35. Issue 6. — P. 1119-1132

1993

• 1 Sobolev V.A., Shchepakina E.A. Self-ignition of dusty media // Combustion, Explosion, and Shock Waves 1993. — Vol. 29. Issue 3. — P. 378-381
• 2 Sobolev V.A., Shchepakina E.A. Autoignition of dust media // Fizika Goreniya i Vzryva 1993. — Vol. 29. Issue 3. — P. 133-136

1992

• 1 Gorelov G.N., Sobolev V.A. Duck-trajectories in a thermal explosion problem // Applied Mathematics Letters 1992. — Vol. 5. Issue 6. — P. 3-6

1990

• 1 Babushok V.I., Goldshtein V.M., Sobolev V.A. Short communication // Combustion Science and Technology 1990. — Vol. 70. Issue 1-3. — P. 81-89

2001

• 1 Shchepakina E., Sobolev V. Integral manifolds, canards and black swans // Nonlinear Analysis, Theory, Methods and Applications 2001. — Vol. 44. Issue 7. — P. 897-908

1988

• 1 Bogatyrev S.V., Sobolev V.A. Separating the rapid and slow motions in the problems of the dynamics of systems of rigid bodies and gyroscopes // Journal of Applied Mathematics and Mechanics 1988. — Vol. 52. Issue 1. — P. 41-48
• 2 Mikheev Yu.V., Sobolev V.A., Fridman E.M. Asymptotic analysis of digital control systems // Avtomatika i Telemekhanika 1988. — Issue 9. — P. 83-88

1987

• 1 Sobolev V.A. Integral manifolds, singular perturbations and optical control // Ukrainian Mathematical Journal 1987. — Vol. 39. Issue 1. — P. 95-99
• 2 Sobolev V.A. INTEGRAL MANIFOLDS AND SOME OPTIMAL CONTROL PROBLEMS. // Periodica Polytechnica, Mechanical Engineering 1987. — Vol. 31. Issue 1. — P. 87-102
• 3 Sobolev V.A. Decomposition of linear singularly perturbed systems // Acta Mathematica Hungarica 1987. — Vol. 49. Issue 3-4. — P. 365-376

1986

• 1 Pendyukhova N.V., Sobolev V.A., Strygin V.V. MOTION OF A RIGID BODY WITH A GYROSCOPE AND A MOVING MASS. // Mechanics of Solids 1986. — Vol. 21. Issue 3. — P. 8-14
• 2 Gol'dshtein V.M., Sobolev V.A., Yablonskii G.S. Relaxation self-oscillations in chemical kinetics: A model, conditions for realization // Chemical Engineering Science 1986. — Vol. 41. Issue 11. — P. 2761-2766

1985

• 1 Sobolev V.A. Fast and Flow Motions of Gyroscopic Systems. // Periodica Polytechnica, Electrical Engineering 1985. — Vol. 29. Issue 1. — P. 57-66

1984

• 1 Sobolev V.A. Integral manifolds and decomposition of singularly perturbed systems // Systems and Control Letters 1984. — Vol. 5. Issue 3. — P. 169-179

1978

• 1 Sobolev V.A., Strygin V.V. PERMISSIBILITY OF CHANGING OVER TO PRECESSIONAL EQUATIONS OF GYROSCOPIC SYSTEMS. // Mech Solids 1978. — Vol. 13. Issue 5. — P. 7-13

1977

• 1 Sobolev V.A., Strygin V.V. ASYMTOTIC METHODS IN THE PROBLEM OF STABILIZATION OF ROTATING BODIES BY USING PASSIVE DAMPERS. // Mech Solids 1977. — Vol. 12. Issue 5. — P. 19-25

2000

• 1 Shchepakina E., Sobolev V. Attracting/Repelling Invariant Manifolds // Stability and Control: Theory and Applications 2000. — № V. 3, Iss. 3. — P. 263-274

2003

• 1 Schneider K.R., Shchepakina E.A., Sobolev V.A. New type of travelling wave solutions // MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2003. — Vol. 26. Issue 16. — P. 1349-1361

2023

• 1 Wang J., Zhang L., Shchepakina E. etc. SOLITARY WAVES OF SINGULARLY PERTURBED GENERALIZED KDV EQUATION WITH HIGH ORDER NONLINEARITY // Discrete and Continuous Dynamical Systems - Series S 2023. — Vol. 16. Issue 3-4. № 3-4. — P. 639-654
• 2 Sobolev V., Shchepakina E. Critical Conditions of a Thermal Explosion in the Case of Autocatalytic Combustion with Account Reagent and Oxidant Consumption // Proceedings of 2023 16th International Conference Management of Large-Scale System Development, MLSD 2023. — 2023. —
• 3 Sobolev V. Reduction of the Optimal Tracking Problem Using PID Control Laws // Proceedings of 2023 16th International Conference Management of Large-Scale System Development, MLSD 2023. — 2023. —
• 4 Sobolev V.A. Decomposition of Singularly Perturbed Optimal Tracking Problems with a Given Reference Trajectory // Journal of Applied and Industrial Mathematics 2023. — Vol. 17. Issue 3. № 3. — P. 640-650
• 5 Antonov D.V., Shchepakina E.A., Sobolev V.A. etc. Dissociation of methane from a layer of methane-hydrate particles: A new simple model // International Journal of Heat and Mass Transfer 2023. — Vol. 213.

2015

• 1 Cantero-Guardeño J.C., Sobolev V., Korobeinikov A. The Spread of Two Viral Strains on a Plant Leaf // Trends in Mathematics 2015. — Vol. 4. — P. 95-99
• 2 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. — Vol. 55. Issue 2. — P. 240-250
• 3 Korobeinikov A., Archibasov A., Sobolev V. Order reduction for an rna virus evolution model // Mathematical Biosciences and Engineering 2015. — Vol. 12. Issue 5. — P. 1007-1016
• 4 Sobolev V.A. Canards and the effect of apparent disappearance // CEUR Workshop Proceedings. — 2015. — Vol. 1490. — P. 190-197

2022

• 1 Sazhin S.S., Shchepakina E., Sobolev V. Critical phenomena in non-adiabatic combustion // Combustion and Flame 2022. — Vol. 245.
• 2 Sobolev V. Dimensional Reduction of Optimal Tracking Problems with a Given Reference Trajectory // Proceedings of 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), STAB 2022. — 2022. —
• 3 Sazhin S.S., Shchepakina E., Sobolev V.A. etc. Puffing/micro-explosion in composite multi-component droplets // International Journal of Heat and Mass Transfer 2022. —
• 4 Sobolev V. GLOBAL INVARIANT MANIFOLDS AND DECOMPOSITION OF ROBOTIC TYPE DYNAMICAL MODELS WITH SINGULAR PERTURBATIONS // Global and Stochastic Analysis 2022. — Vol. 9. Issue 3. № 3. — P. 19-26
• 5 Tonini S., Cossali G.E., Shchepakina E.A. etc. A model of droplet evaporation: New mathematical developments // Physics of Fluids 2022. — Vol. 34. Issue 7. № 7.

2021

• 1 Makarov D., Sobolev V. Decomposition of Multiple Time-Scale Systems // Proceedings of 2021 14th International Conference Management of Large-Scale System Development, MLSD 2021. — 2021. —
• 2 Zhang L., Wang J., Shchepakina E. etc. New type of solitary wave solution with coexisting crest and trough for a perturbed wave equation // Nonlinear Dynamics 2021. —
• 3 Sobolev V.A. Critical traveling wave solution in the Meinhardt type model // Journal of Physics: Conference Series. — 2021. — Vol. 1745. Issue 1.
• 4 Shchepakina E., Sobolev V., Sazhin S.S. Dynamics of spray combustion in diesel engine-like conditions // 2021 International Scientific and Technical Engine Conference (EC). — 2021. — P. 1-6

2020

• 1 Korobeinikov A., Shchepakina E., Sobolev V. A black swan and canard cascades in an SIR infectious disease model // Mathematical Biosciences and Engineering 2020. — Vol. 17. Issue 1. — P. 725-736
• 2 Voropaeva N., Sobolev V. PD-Regulators Design Problem for Robotic Type Systems with Singular Perturbations // Proceedings of ITNT 2020 - 6th IEEE International Conference on Information Technology and Nanotechnology. — 2020. —
• 3 Voropaeva Nataliya Vladimirovna, Sobolev V.A. Decomposition of PD-regulators design problem for systems with slow and fast modes // VI Международная конференция и молодёжная школа «Информационные технологии и нанотехнологии» (ИТНТ-2020). — 2020. — Vol. 3. — P. 810-812
• 4 Korobeinikov A., Shchepakina E., Sobolev V. The paradox of enrichment, spatial heterogeneity, community effects and the phenomenon of apparent disappearance in the marine bacteriophage dynamics // ANZIAM journal 2020. — Vol. 62. Issue 4. — P. 453-468
• 5 Sobolev V. Decomposition of Traveling Wave Existence Problem for Singularly Perturbed Equations // Proceedings of ITNT 2020 - 6th IEEE International Conference on Information Technology and Nanotechnology. — 2020. —

2019

• 1 Tropkina E., Sobolev V. Slow Invariant Manifolds in the Problem of Order Reduction of Singularly Perturbed Systems // Trends in Mathematics 2019. — Vol. 11. — P. 125-129
• 2 Sazhin S.S., Shchepakina E., Sobolev V. Parameterisations of slow invariant manifolds: application to a spray ignition and combustion model // JOURNAL OF ENGINEERING MATHEMATICS 2019. — Vol. 114. Issue 1.
• 3 Shchepakina E., Sobolev V., Zhang L. Critical travelling wave solution in one singularly perturbed parabolic equation // Journal of Physics: Conference Series. — 2019. — Vol. 1368. Issue 4.
• 4 Kobrin A., Sobolev V. Constructive Method of Decomposition in Singularly Perturbed Problems of Non-holonomic Mechanics // Trends in Mathematics 2019. — Vol. 11. — P. 1-6
• 5 Sobolev V. Cheap Control Problem in a Critical Case // Trends in Mathematics 2019. — Vol. 11. — P. 295-299
• 6 Sobolev V. Efficient decomposition of singularly perturbed systems // MATHEMATICAL MODELLING OF NATURAL PHENOMENA 2019. — Vol. 14. Issue 4.
• 7 Sazhin S., Shchepakina E., Sobolev V. Modelling of sprays: Simple solutions of complex problems // Journal of Physics: Conference Series. — 2019. — Vol. 1368. Issue 4.
• 8 Semenov M.E., Reshetova O.O., Sobolev V.A. etc. The van der Pol oscillator under hysteretic control: Regular and chaotic dynamics // Journal of Physics: Conference Series. — 2019. — Vol. 1368. Issue 4.
• 9 Sobolev V. Decomposition of enzyme kinetics equations // Journal of Physics: Conference Series. — 2019. — Vol. 1368. Issue 4.

2018

• 1 Sobolev V., Shchepakina E. Cheap control problem for micro drone quadcopter // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.
• 2 Sobolev V.A. Thrice critical case in singularly perturbed control problems // Trends in Mathematics 2018. — Vol. 10. — P. 83-87
• 3 Sazhin S.S., Shchepakina E., Sobolev V. Order reduction in models of spray ignition and combustion // Combustion and Flame 2018. — Vol. 187. — P. 122-128
• 4 Osintcev M., Sobolev V.A. Order reduction of Kalman–Bucy filter for systems with low measurement noise // Trends in Mathematics 2018. — Vol. 10. — P. 47-52
• 5 Sazhin S.S., Shchepakina E., Sobolev V. Modelling of sprays: Recent results and future challenges // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.
• 6 Kobrin A., Sobolev V. Decomposition of nonholonomic mechanics models // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.
• 7 Yudaev S.A., Rachinskii D., Sobolev V.A. Asymptotic solution for a biped walker model // Trends in Mathematics 2018. — Vol. 10. — P. 95-99
• 8 Shchepakina E., Sobolev V. Cascade of 3D canard doublets // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.

2017

• 1 Sazhin S.S., Shchepakina E., Sobolev V. Positively invariant manifolds: Concept and applications // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.
• 2 Sobolev V. One Critical Case in Singularly Perturbed Control Problems // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.
• 3 Shchepakina E., Sobolev V. Conditions for the loss of stability of eqiulibrium manifold in satellite model // CEUR Workshop Proceedings. — 2017. — Vol. 1904. — P. 49-51
• 4 Aksenova N., Sobolev V. Control of a one rigit-link manipulator in the case of non-smooth periodic trajectory // CEUR Workshop Proceedings. — 2017. — Vol. 1904. — P. 40-42
• 5 Kobrin A., Sobolev V. Integral manifolds of fast-slow systems in nonholonomic mechanics // Procedia Engineering. — 2017. — Vol. 201. — P. 556-560
• 6 Osintcev M., Sobolev V. Regularization of the matrix Riccati equation in optimal estimation problem with low measurement noise // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.
• 7 Yudaev S.A., Rachinskii D., Sobolev V.A. An asymptotic solution to a passive biped walker model // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.

2016

• 1 Korobeinikov A., Shchepakina E., Sobolev V. Paradox of enrichment and system order reduction: Bacteriophages dynamics as case study // Mathematical Medicine and Biology 2016. — Vol. 33. Issue 3. — P. 359-369
• 2 Sobolev V. Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases // Journal of Physics: Conference Series. — 2016. — Vol. 727. Issue 1.
• 3 Shchepakina E., Sobolev V. Invariant surfaces of variable stability // Journal of Physics: Conference Series. — 2016. — Vol. 727. Issue 1.
• 4 Archibasov A.A., Korobeinikov A., Sobolev V.A. Passage to the limit in a singularly perturbed partial integro-differential system // Differential Equations 2016. — Vol. 52. Issue 9. — P. 1115-1122
• 5 Korobeinikov A., Archibasov A., Sobolev V. Multi-scale problem in the model of RNA virus evolution // Journal of Physics: Conference Series. — 2016. — Vol. 727. Issue 1.
• 6 Sobolev V.A. Critical cases in slow/fast control problems // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 742-753
• 7 Aksenova N.K., Sobolev V.A. Control of a one rigit-link manipulator in the case of nonsmooth trajectory // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 493-497
• 8 Nekhozhina Ju.G., Sobolev V.A. Andronov-Hopf's bifurcation in a dynamic model of cell population // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 636-641

2014

• 1 Shchepakina E., Sobolev V., Mortell M.P. Introduction // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 1-23
• 2 Shchepakina E., Sobolev V., Mortell M.P. Reduction methods for chemical systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 111-117
• 3 Shchepakina E., Sobolev V., Mortell M.P. Canards and black swans // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 141-182
• 4 Shchepakina E., Sobolev V., Mortell M.P. The book of numbers // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 43-80
• 5 Shchepakina E., Sobolev, V, Mortell M. P. Singular Perturbations: Introduction to System Order Reduction Methods with Applications // SINGULAR PERTURBATIONS: INTRODUCTION TO SYSTEM ORDER REDUCTION METHODS WITH APPLICATIONS 2014. — Vol. 2114.
• 6 Shchepakina E., Sobolev V., Mortell M.P. Reduction methods for chemical systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 111-117
• 7 Shchepakina E., Sobolev V., Mortell M.P. Specific cases // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 119-139
• 8 Shchepakina, Elena, Sobolev, Vladimir, Mortell Michael P. Proofs // SINGULAR PERTURBATIONS: INTRODUCTION TO SYSTEM ORDER REDUCTION METHODS WITH APPLICATIONS 2014. — Vol. 2114. — P. 183-198
• 9 Shchepakina E., Sobolev V., Mortell M.P. Appendix: Proofs // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 183-198
• 10 Shchepakina E., Sobolev V., Mortell M.P. Singular singularly perturbed systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 93-110
• 11 Shchepakina Elena, Sobolev, Vladimir, Mortell Michael P. Singular Perturbations Introduction to System Order Reduction Methods with Applications Introduction // SINGULAR PERTURBATIONS: INTRODUCTION TO SYSTEM ORDER REDUCTION METHODS WITH APPLICATIONS 2014. — Vol. 2114. — P. 1-23
• 12 Korobeinikov A., Sobolev V. The phenomenon of apparent disappearance in the marine bacteriophage dynamics // Trends in Mathematics 2014. — Vol. 2. — P. 109-113
• 13 Mortell Michael P., Shchepakina, Elena, Sobolev, Vladimir Singular Perturbations Introduction to System Order Reduction Methods with Applications Preface // SINGULAR PERTURBATIONS: INTRODUCTION TO SYSTEM ORDER REDUCTION METHODS WITH APPLICATIONS 2014. — Vol. 2114. — P. IX-+
• 14 Shchepakina E., Sobolev V., Mortell M.P. Canards and black swans // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 141-182
• 15 Osintsev M., Sobolev V. Global invariant manifolds in a problem of Kalman-Bucy filtering for gyroscopic systems // Global and Stochastic Analysis 2014. — Vol. 1. Issue 1. — P. 103-124
• 16 Shchepakina E., Sobolev V., Mortell M.P. Slow integral manifolds // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 25-42
• 17 Sobolev V., Korobeinikov A. System order reduction methods with application to a bacteriophages dynamics model // Trends in Mathematics 2014. — Vol. 2. — P. 121-125
• 18 Shchepakina E., Sobolev V., Mortell M.P. Singular Singularly Perturbed Systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 93-110
• 19 Shchepakina E., Sobolev V., Mortell M.P. Appendix: Proofs // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 183-198
• 20 Shchepakina E., Sobolev V., Mortell M.P. Representations of slow integral manifolds // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 81-92
• 21 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. — Vol. 54. Issue 1. — P. 45-58
• 22 Shchepakina E., Sobolev V., Mortell M.P. The book of numbers // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 43-80

2005

• 1 Sobolev, V Geometry of singular perturbations: Critical cases // Singular Perturbations and Hysteresis. — 2005. — P. 153-206
• 2 Kitaeva E.V., Sobolev V.A. Numerical determination of bounded solutions to discrete singularly perturbed equations and critical combustion regimes // Computational Mathematics and Mathematical Physics 2005. — Vol. 45. Issue 1. — P. 52-82
• 3 Smetannikova E.N., Sobolev V.A. Regularization of cheap periodic control problems // Automation and Remote Control 2005. — Vol. 66. Issue 6. — P. 903-916
• 4 Pokrovskii A, Sobolev, V A naive view of time relaxation and hysteresis // Singular Perturbations and Hysteresis. — 2005. — P. 1-+
• 5 Martins J.A.C., Marques M.D.P.M., Petrov A. etc. (In)stability of quasi-static paths of some finite dimensional smooth or elastic-plastic systems // Journal of Physics: Conference Series 2005. — Vol. 22. Issue 1. — P. 124-138
• 6 Smetannikova E.N., Sobolev V.A. A periodic singularly perturbed problem for the matrix riccati equation // Differential Equations 2005. — Vol. 41. Issue 4. — P. 529-537
• 7 Sobolev V.A., Schneider K., Shchepakina E.A. Three kinds of waves of non-adiabatic combustion in case of autocatalytic reaction // Khimicheskaya Fizika 2005. — Vol. 24. Issue 6. — P. 63-70
• 8 Shchepakina E., Sobolev V. Black swans and canards in laser and combustion models. In: Singular Perturbations and HysteresisPhiladelphia: SIAM, 2005. 55p.
• 9 Mortell M.P., O'Malley R.E., Pokrovskii A. etc. Singular perturbations and hysteresisPhiladelphia: SIAM, 2005. 358p.

2013

• 1 Sobolev V. Canard cascades // Discrete and Continuous Dynamical Systems - Series B 2013. — Vol. 18. Issue 2. — P. 513-521
• 2 Osintsev M.S., Sobolev V.A. Dimensionality reduction in optimal control and estimation problems for systems of solid bodies with low dissipation // Automation and Remote Control 2013. — Vol. 74. Issue 8. — P. 1334-1347

2012

• 1 Sobolev V.A., Tropkina E.A. Asymptotic expansions of slow invariant manifolds and reduction of chemical kinetics models // Computational Mathematics and Mathematical Physics 2012. — Vol. 52. Issue 1. — P. 75-89
• 2 Osintsev M., Sobolev V. Slow integral manifolds in control and graduate education in Samara // IFAC Proceedings Volumes (IFAC-PapersOnline). — 2012. — Vol. 45. Issue 11 PART 1. — P. 45-50

2011

• 1 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
• 2 Pokrovskii A., Rachinskii D., Sobolev V. etc. Topological degree in analysis of canard-type trajectories in 3-D systems // Applicable Analysis 2011. — Vol. 90. Issue 7. — P. 1123-1139

2010

• 1 Sazhin S.S., Shchepakina E., Sobolev V. Order reduction of a non-Lipschitzian model of monodisperse spray ignition // Mathematical and Computer Modelling 2010. — Vol. 52. Issue 3-4. — P. 529-537
• 2 Rachinskii D., Shchepakina E., Sobolev, V. In Memory of Alexei Pokrovskii: Systems with Hysteresis & Murphys, 10 Years Later // 15TH INTERNATIONAL CONFERENCE ON STRANGENESS IN QUARK MATTER (SQM2015). — 2010. — Vol. 268.

2008

• 1 Pokrovskii A., Shchepakina E., Sobolev V. Canard doublet in a Lotka-Volterra type model // Journal of Physics: Conference Series 2008. — Vol. 138.
• 2 Shchepakina E., Sobolev V. Modelling of critical phenomena for ignition of metal particles // Journal of Physics: Conference Series 2008. — Vol. 138.
• 3 Sazhin S., Shakked T., Sobolev V. etc. Particle grouping in oscillating flows // European Journal of Mechanics, B/Fluids 2008. — Vol. 27. Issue 2. — P. 131-149

2007

• 1 Rebrova N.V., Martins J.A.C., Sobolev V.A. Mathematical results on the stability of quasi-static paths of smooth systems // Topics on Mathematics for Smart Systems - Proceedings of the European Conference. — 2007. — P. 183-192

2006

• 1 Gorelov G.N., Shchepakina E.A., Sobolev V.A. Canards and critical behavior in autocatalytic combustion models // JOURNAL OF ENGINEERING MATHEMATICS 2006. — Vol. 56. Issue 2. — P. 143-160
• 2 Martins J.A.C., Rebrova N.V., Sobolev V.A. On the (in)stability of quasi-static paths of smooth systems: Definitions and sufficient conditions // MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2006. — Vol. 29. Issue 6. — P. 741-750
• 3 Schneider K.R., Shchetinina E., Sobolev V.A. Control of integral manifolds loosing their attractivity in time // Journal of Mathematical Analysis and Applications 2006. — Vol. 315. Issue 2. — P. 740-757
• 4 Gavin C., Pokrovskii A., Prentice M. etc. Dynamics of a Lotka-Volterra type model with applications to marine phage population dynamics // Journal of Physics: Conference Series. — 2006. — Vol. 55. Issue 1. — P. 80-93
• 5 Voropaeva N.V., Sobolev V.A. Decomposition of a linear-quadratic optimal control problem with fast and slow variables // Automation and Remote Control 2006. — Vol. 67. Issue 8. — P. 1185-1193

1976

• 1 Strygin V.V., Sobolev V.A. EFFECT OF GEOMETRIC AND KINETIC PARAMETERS AND ENERGY DISSIPATION ON THE ORIENTATION STABILITY OF SATELLITES WITH DOUBLE SPIN. // Cosmic Res 1976. — Vol. 14. Issue 3. — P. 331-335