Shchepakina, Elena A.

2024

• 1 Zhang L., Wang J., Shchepakina E. etc. New solitary waves in a convecting fluid // Chaos, Solitons and Fractals 2024. — Vol. 183.
• 2 Salman S.M., Shchepakina E. On the slow–fast dynamics of a tri-trophic food chain model with fear and Allee effects // MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2024. —
• 3 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.
• 4 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
• 5 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.

2009

• 1 Golodova E.S., Shchepakina E.A. Modeling of safe combustion at the maximum temperature // Mathematical Models and Computer Simulations 2009. — Vol. 1. Issue 2. — P. 322-334

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

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

1998

• 1 Shchepakina E. Duck-trajectories in Combustion Problems // International Congress of Mathematicians (ICM-1998). — 1998. — P. 332-332

2000

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

2001

• 1 Shchepakina E.A. Critical conditions of self-ignition in porous medium // Khimicheskaya Fizika 2001. — Vol. 20. Issue 7. — P. 3-10
• 2 Shchepakina E., Sobolev V. Integral manifolds, canards and black swans // Nonlinear Analysis, Theory, Methods and Applications 2001. — Vol. 44. Issue 7. — P. 897-908

2002

• 1 Shchepakina E.A. Slow integral manifolds with stability change in the case of a fast vector variable // Differential Equations 2002. — Vol. 38. Issue 10. — P. 1446-1452

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
• 2 Shchepakina E. Black swans and canards in self-ignition problem // Nonlinear Analysis: Real World Applications 2003. — Vol. 4. Issue 1. — P. 45-50

2004

• 1 Shchepakina E.A. Two forms of stability change for integral manifolds // Differential Equations 2004. — Vol. 40. Issue 5. — P. 766-769

2005

• 1 Shchepakina E., Sobolev V. Black swans and canards in laser and combustion models. In: Singular Perturbations and HysteresisPhiladelphia: SIAM, 2005. 55p.
• 2 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
• 3 Shchepakina E. Canards and black swans in a model of a 3-D autocatalator // Journal of Physics: Conference Series 2005. — Vol. 22. Issue 1. — P. 194-207

2006

• 1 Golodova E., Shchepakina E. Maximal combustion temperature estimation // Journal of Physics: Conference Series. — 2006. — Vol. 55. Issue 1. — P. 94-104
• 2 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

2008

• 1 Shchepakina E., Sobolev V. Modelling of critical phenomena for ignition of metal particles // Journal of Physics: Conference Series 2008. — Vol. 138.
• 2 Pokrovskii A., Shchepakina E., Sobolev V. Canard doublet in a Lotka-Volterra type model // Journal of Physics: Conference Series 2008. — Vol. 138.

2010

• 1 Shchepakina E., Rachinskii D. In Memory of Alexei Pokrovskii: Systems with Hysteresis & Murphys, 10 Years Later // Journal of Physics: Conference Series 2010. — № v. 268. — P. 1-6
• 2 Korotkova O., Shchepakina E. Color changes in stochastic light fields propagating in non-Kolmogorov turbulence // Optics Letters 2010. — Vol. 35. Issue 22. — P. 3772-3774
• 3 Korotkova O., SchEPAKINA E.A. Color changes in sto-chastic light fields propaga-ting in non-Kolmogorov turbu-lence // Optics Letters 2010. — № Vol. 35, Issue 22. — P. 3772-3774
• 4 Shchepakina E., Korotkova O. Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence // Optics Express 2010. — Vol. 18. Issue 10. — P. 10650-10658
• 5 Shchepakina E., Korotkova O. Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence // Optics Express 2010. — Vol. 18. Issue 10. — P. 10650-10658
• 6 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

2023

• 1 Shchepakina E.A., Zubrilin I.A., Kuznecov A.Yu. etc. Physical and Chemical Features of Hydrogen Combustion and Their Influence on the Characteristics of Gas Turbine Combustion Chambers // Applied Sciences (Switzerland) 2023. — Vol. 13. Issue 6. № 6.
• 2 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
• 3 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. —
• 4 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.

2011

• 1 Shchepakina E., Korotkova O. Condition for canard explosion in a semiconductor optical amplifier // Journal of the Optical Society of America B: Optical Physics 2011. — Vol. 28. Issue 8. — P. 1988-1993
• 2 SchEPAKINA E.A., Korotkova O. Control of the canard explosion in a semiconductor optical amplifier // Международная конференция Дифференциальные урав-нения и смежные вопросы , посвященная 110-й годовщине со дня рождения И.Г. Петровского, Сборник тезисов.. — 2011. — P. 108-109
• 3 Shchepakina E., Farwell N., Korotkova O. Spectral changes in stochastic light beams propagating in turbulent ocean // Applied Physics B: Lasers and Optics 2011. — Vol. 105. Issue 2. — P. 415-420

2012

• 1 Korotkova O., Sahin S., Shchepakina E. Multi-Gaussian Schell-model beams // Journal of the Optical Society of America A: Optics and Image Science, and Vision 2012. — Vol. 29. Issue 10. — P. 2159-2164
• 2 Korotkova O., Farwell N., Shchepakina E. Light scintillation in oceanic turbulence // Waves in Random and Complex Media 2012. — Vol. 22. Issue 2. — P. 260-266

2013

• 1 Korotkova O., Shchepakina E. Tuning the spectral composition of random beams propagating in free space and in a turbulent atmosphere // Journal of Optics 2013. — Vol. 15. Issue 7.
• 2 Mei Z., Korotkova O., Shchepakina E. Electromagnetic multi-Gaussian Schell-model beams // Journal of Optics 2013. — Vol. 15. Issue 2.
• 3 Shchepakina E., Korotkova O. Spectral Gaussian Schell-model beams // Optics Letters 2013. — Vol. 38. Issue 13. — P. 2233-2236
• 4 Shchepakina E., Korotkova O. Canard explosion in chemical and optical systems // Discrete and Continuous Dynamical Systems - Series B 2013. — Vol. 18. Issue 2. — P. 495-512
• 5 Korotkova O., Shchepakina E. Manipulation of spectral composition of a random beam in turbulent atmosphere // Optics InfoBase Conference Papers. — 2013. —

2014

• 1 Shchepakina E., Sobolev V., Mortell M.P. Singular Singularly Perturbed Systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 93-110
• 2 Shchepakina E., Sobolev V., Mortell M.P. The book of numbers // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 43-80
• 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. Introduction // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 1-23
• 6 Shchepakina E., Sobolev V., Mortell M.P. Canards and black swans // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 141-182
• 7 Shchepakina E., Sobolev V., Mortell M.P. Representations of slow integral manifolds // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 81-92
• 8 Shchepakina E., Sobolev V., Mortell M.P. Reduction methods for chemical systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 111-117
• 9 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-+
• 10 Shchepakina E. Representations of slow integral manifolds // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 81-92
• 11 Shchepakina E., Sobolev V., Mortell M.P. Singular singularly perturbed systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 93-110
• 12 Shchepakina, Elena, Sobolev, Vladimir, Mortell Michael P. Proofs // SINGULAR PERTURBATIONS: INTRODUCTION TO SYSTEM ORDER REDUCTION METHODS WITH APPLICATIONS 2014. — Vol. 2114. — P. 183-198
• 13 Korotkova O., Shchepakina E. Random sources for optical frames // Optics Express 2014. — Vol. 22. Issue 9. — P. 10622-10633
• 14 Korotkova O., Shchepakina E. Rectangular multi-gaussian schell-model beams in atmospheric turbulence // Journal of Optics 2014. — Vol. 16. Issue 4.
• 15 Shchepakina E., Sobolev V., Mortell M.P. Appendix: Proofs // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 183-198
• 16 Shchepakina E., Sobolev V., Mortell M.P. Specific cases // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 119-139
• 17 Shchepakina E., Sobolev V., Mortell M.P. Slow integral manifolds // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 25-42
• 18 Korotkova O., Sahin S., Shchepakina E. Light scattering by three-dimensional objects with semi-hard boundaries // Journal of the Optical Society of America A: Optics and Image Science, and Vision 2014. — Vol. 31. Issue 8. — P. 1782-1787
• 19 Shchepakina E., Sobolev V., Mortell M.P. Reduction methods for chemical systems // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 111-117
• 20 Shchepakina E., Sobolev V., Mortell M.P. Appendix: Proofs // Lecture Notes in Mathematics 2014. — Vol. 2114. — P. 183-198

2015

• 1 Shchepakina E.A. Critical phenomena in a model of fuel's heating in a porous medium // CEUR Workshop Proceedings. — 2015. — Vol. 1490. — P. 179-189

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 Soifer V.A., Korotkova O., Khonina S.N. etc. Vortex beams in turbulent media: Review // Computer Optics 2016. — Vol. 40. Issue 5. — P. 605-624
• 3 Shchepakina E., Sobolev V. Invariant surfaces of variable stability // Journal of Physics: Conference Series. — 2016. — Vol. 727. Issue 1.
• 4 Lapshova M.A., Shchepakina E.A. Study of the dynamical model of HIV // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 600-609
• 5 Shchepakina E.A. Three scenarios for changing of stability in the dynamic model of nerve conduction // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 664-673
• 6 Agataeva A.Zh., Shchepakina E.A. Critical conditions of ignition of fuel spray containing liquid fuel droplets // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 484-492
• 7 Firstova N., Shchepakina E. Study of oscillatory processes in the one model of electrochemical reactor // CEUR Workshop Proceedings. — 2016. — Vol. 1638. — P. 731-741

2017

• 1 Shchepakina E. Calculation of Maximum Safe Temperature of Fuel's Heating in a Porous Medium // Procedia Engineering. — 2017. — Vol. 201. — P. 468-477
• 2 Firstova N., Shchepakina E. Modelling of Critical Conditions for an Electrochemical Reactor Model // Procedia Engineering. — 2017. — Vol. 201. — P. 495-502
• 3 Vidilina O., Shchepakina E. Calculation of critical conditions for the filtration combustion model // CEUR Workshop Proceedings. — 2017. — Vol. 1904. — P. 151-157
• 4 Tropkina E., Shchepakina E. Study of a singularly perturbed tuberculosis model // CEUR Workshop Proceedings. — 2017. — Vol. 1904. — P. 117-123
• 5 Sazhin S.S., Shchepakina E., Sobolev V. Positively invariant manifolds: Concept and applications // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.
• 6 Shchepakina E. Stable/unstable slow integral manifolds in critical cases // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.
• 7 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
• 8 Firstova N., Shchepakina E. Conditions for the critical phenomena in a dynamic model of an electrocatalytic reaction // Journal of Physics: Conference Series. — 2017. — Vol. 811. Issue 1.

2018

• 1 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
• 2 Sobolev V., Shchepakina E. Cheap control problem for micro drone quadcopter // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.
• 3 Shchepakina E., Sobolev V. Cascade of 3D canard doublets // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.
• 4 Agataeva A.Z., Shchepakina E.A. Analysis of the threshold phenomena in a dynamic model of a fuel spray ignition // Journal of Physics: Conference Series. — 2018. — Vol. 1096. Issue 1.
• 5 Shchepakina E. Self-Ignition in Porous Media: Critical Phenomena // IOP Conference Series: Materials Science and Engineering. — 2018. — Vol. 302. Issue 1.
• 6 Shchepakina E. Delayed stability loss scenarios for a slow integral manifold // Trends in Mathematics 2018. — Vol. 10. — P. 71-75
• 7 Shchepakina E. A geometric approach to the modelling of critical phenomena for a spray combustion model // MATEC Web of Conferences. — 2018. — Vol. 209.
• 8 Shchepakina E., Firstova N. Critical phenomena in a dynamic model of electrocatalytic reaction // Trends in Mathematics 2018. — Vol. 10. — P. 77-81
• 9 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.

2019

• 1 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.
• 2 Firstova N., Shchepakina E. Critical Phenomena in a Dynamical System Under Random Perturbations // Trends in Mathematics 2019. — Vol. 11. — P. 259-263
• 3 Matveev S.S., Idrisov D.V., Gurakov N. I. etc. Simulation of CO and CO2 emissions in model combustion chamber based on the combination les and Reactor Network model // E3S Web of Conferences. — 2019. — Vol. 80.
• 4 Shchepakina E. A New Approach to Canards Chase in 3D // Trends in Mathematics 2019. — Vol. 11. — P. 119-123
• 5 Sazhin S., Shchepakina E., Sobolev V. Modelling of sprays: Simple solutions of complex problems // Journal of Physics: Conference Series. — 2019. — Vol. 1368. Issue 4.
• 6 Shchepakina E. Black swans and canards in two predator – One prey model // MATHEMATICAL MODELLING OF NATURAL PHENOMENA 2019. — Vol. 14. Issue 4.
• 7 Shchepakina E. Repulsive Invariant Manifolds in Modeling the Critical Phenomena // Trends in Mathematics 2019. — Vol. 11. — P. 113-117
• 8 Shchepakina E. Modelling of oscillations in slow/fast models of population dynamics // Journal of Physics: Conference Series. — 2019. — Vol. 1368. Issue 4.
• 9 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.

2020

• 1 Shchepakina E. Critical Traveling Waves in a Flow Reactor Model // Proceedings of ITNT 2020 - 6th IEEE International Conference on Information Technology and Nanotechnology. — 2020. —
• 2 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
• 3 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
• 4 Shchepakina E. Canard Traveling Waves in a Reaction-Diffusion Model // Proceedings of ITNT 2020 - 6th IEEE International Conference on Information Technology and Nanotechnology. — 2020. —

2021

• 1 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. —
• 2 Shchepakina E. Order reduction for critical traveling wave problems // Journal of Physics: Conference Series. — 2021. — Vol. 1745. Issue 1.
• 3 Shchepakina E., Tropkina E. Order reduction for problems with traveling wave solutions to reaction-diffusion systems // 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

2022

• 1 Sazhin S.S., Shchepakina E., Sobolev V. Critical phenomena in non-adiabatic combustion // Combustion and Flame 2022. — Vol. 245.
• 2 Shchepakina E. Unstable Invariant Manifolds in a Control Problem of the Combustion Process of a Gas Mixture // Proceedings of 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), STAB 2022. — 2022. —
• 3 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.
• 4 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. —

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