Mathematical modeling of reacting flows. Stability of shock waves. Stability of flows with phase transitions in a porous medium.
Biography
Graduated from Moscow Engineering Physics Institute 1981 (department of chemical physics).
Ph.D. thesis was defended in 1987. D.Sci. thesis was defended in 2021. A list of my work contains about 50 titles.
Main publications:
V. A. Shargatov, “Dynamics and stability of air bubbles in a porous medium”, Comput. Math. Math. Phys.,, 58 (2018), 1172-1187
A. T. Il'ichev, V. A. Shargatov, Y. B. Fu, “Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube”, Acta Mech, 231 (2020), 4095–4110
A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “On the Structure Stability of a Neutrally Stable Shock Wave in a Gas and on Spontaneous Emission of Perturbations”, J. Exp. Theor. Phys, 131:3 (2020), 481–495
A.P. Chugainova, V.A. Shargatov, “Analytical description of the structure of special discontinuities described by a generalized KdV–Burgers equation”, Commun. Nonlinear Sci. Numer. Simul., 66 (2019), 129-146
G.G. Tsypkin, V.A. Shargatov, “Influence of capillary pressure gradient on connectivity of flow through a porous medium”, International Journal of Heat and Mass Transfer, 127 (2018), 1053-1063
Vladimir A. Shargatov, Anna P. Chugainova, Georgy V. Kolomoitsev, Irik I. Nasyrov, Anastasia M. Tomasheva, Sergey V. Gorkunov, Polina I. Kozhurina, “Why stable finite-difference schemes can converge to different solutions: analysis for the generalized hopf equation”, Computation, 12:4 (2024), 76–15
2023
2.
V. A. Shargatov, A. P. Chugainova, A. M. Tomasheva, “Structures of Classical and Special Discontinuities for the Generalized Korteweg–de Vries–Burgers Equation in the Case of a Flux Function with Four Inflection Points”, Trudy Mat. Inst. Steklova, 322 (2023), 266–281; Proc. Steklov Inst. Math., 322 (2023), 257–272
V. A. Shargatov, A. P. Chugainova, G. V. Kolomiytsev, “Global stability of traveling wave solutions of generalized Korteveg–de Vries–Burgers equation with non-constant dissipation parameter”, J. Comput. Appl. Math., 412 (2022), 114354–18
A. T. Il'ichev, V. A. Shargatov, “Stability of the aneurysm-type solution in a membrane tube with localized wall thinning filled with a fluid with a non-constant velocity profile”, J. Fluids Struct., 114 (2022), 103712–12
5.
A. P. Chugainova, G. V. Kolomoitsev, V. A. Shargatov, “On the Instability of Monotone Traveling-Wave Solutions for a Generalized Korteweg-–de Vries-–Burgers Equation”, Russ. J. Math. Phys., 29 (2022), 342–357
A. T. Il'ichev, V. A. Shargatov, “Stability of an aneurysm in a membrane tube filled with an ideal fluid”, TMF, 211:2 (2022), 236–248; Theoret. and Math. Phys., 211:2 (2022), 642–652
2021
7.
V. A. Shargatov, A. P. Chugainova, “Stability analysis of traveling wave solutions of a generalized Korteweg–de Vries–Burgers equation with variable dissipation parameter”, J. Comput. Appl. Math., 397 (2021), 113654–17
A. T. Il'ichev, V. A. Shargatov, Y. B. Fu, “Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube”, Acta Mech., 231 (2020), 4095–4110
Vladimir A. Shargatov, Sergey V. Gorkunov, Andrej T. Il'ichev, “Stability of finite perturbations of the phase transition interface for one problem of water evaporation in a porous medium”, Appl. Math. Comput., 378 (2020), 152208–17
A. P. Chugainova, V. A. Shargatov, “Traveling waves and undercompressive shocks in solutions of the generalized Korteweg–de Vries–Burgers equation with a time-dependent dissipation coefficient distribution”, Eur. Phys. J. Plus, 135:8 (2020), 1–18
S. V. Gorkunov, A. T. Il'ichev, V. A. Shargatov, “Critical evolution of finite perturbations of a water evaporation surface in porous media”, Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2020, no. 2, 61–69; Fluid Dyn., 55:2 (2020), 204–212
12.
A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “On the Structure Stability of a Neutrally Stable Shock Wave in a Gas and on Spontaneous Emission of Perturbations”, Zh. Èksper. Teoret. Fiz., 158:3 (2020), 544–560; J. Exp. Theor. Phys., 131:3 (2020), 481–495
V. A. Shargatov, A. T. Il'ichev, “Dynamics of Perturbations under Diffusion in a Porous Medium”, Trudy Mat. Inst. Steklova, 310 (2020), 309–321; Proc. Steklov Inst. Math., 310 (2020), 291–303
2019
14.
A. P. Chugainova, V. A. Shargatov, “Study of nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation”, AIP Conf. Proc., 2164 (2019), 50002, 8 pp.
V. A. Shargatov, S. V. Gorkunov, A. T. Il'ichev, “Dynamics of front-like water evaporation phase transition interfaces”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 223–236
A.P. Chugainova, V.A. Shargatov, “Analytical description of the structure of special discontinuities described by a generalized KdV–Burgers equation”, Commun. Nonlinear Sci. Numer. Simul., 66 (2019), 129–146
17.
A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “Spontaneously radiating shock waves”, Dokl. Akad. Nauk, 487:1 (2019), 28–31; Doklady Physics, 64:7 (2019), 293–296
18.
A. P. Chugainova, A. T. Il'ichev, V. A. Shargatov, “Stability of shock wave structures in nonlinear elastic media”, Math. Mech. Solids, 24:11 (2019), 3456–3471
A. P. Chugainova, V. A. Shargatov, S. V. Gorkunov, S. I. Sumskoi, “Regimes of shock wave propagation through comb-shaped obstacles”, AIP Conf. Proc., 2025 (2018), 80002
20.
V. A. Shargatov, A. P. Chugainova, S. V. Gorkunov, S. I. Sumskoi, “Analytical and numerical solutions of the shock tube problem in a channel with a pseudo-perforated wall”, JPCS, 1099 (2018), 12013, 8 pp.
V. A. Shargatov, A. P. Chugainova, S. V. Gorkunov, S. I. Sumskoi, “Flow structure behind a shock wave in a channel with periodically arranged obstacles”, Trudy Mat. Inst. Steklova, 300 (2018), 216–228; Proc. Steklov Inst. Math., 300 (2018), 206–218
A. T. Il'ichev, S. I. Sumskoi, V. A. Shargatov, “Unsteady flows in deformable pipes: the energy conservation law”, Trudy Mat. Inst. Steklova, 300 (2018), 76–85; Proc. Steklov Inst. Math., 300 (2018), 68–77
23.
V. A. Shargatov, “Dynamics and stability of air bubbles in a porous medium”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1219–1234; Comput. Math. Math. Phys., 58:7 (2018), 1172–1187
Anna P. Chugainova, Andrey T. Il'ichev, Andrey G. Kulikovskii, Vladimir A. Shargatov, “Problem of arbitrary discontinuity disintegration for the generalized Hopf equation: selection conditions for a unique solution”, J. Appl. Math., 82:3 (2017), 496, 525 pp.
A. G. Kulikovskii, A. P. Chugainova, V. A. Shargatov, “Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1363–1370; Comput. Math. Math. Phys., 56:7 (2016), 1355–1362
A. P. Chugainova, V. A. Shargatov, “Stability of discontinuity structures described by a generalized KdV–Burgers equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016), 259–274; Comput. Math. Math. Phys., 56:2 (2016), 263–277
A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “Spectral stability of special discontinuities”, Dokl. Akad. Nauk, 462:5 (2015), 512–516; Dokl. Math., 91:3 (2015), 347–351
V. A. Shargatov, A. T. Il'ichev, G. G. Tsypkin, “Dynamics and stability of moving fronts of water evaporation in a porous medium”, Int. J. Heat Mass Transfer, 83 (2015), 552–561
A. P. Chugainova, V. A. Shargatov, “Stability of nonstationary solutions of the generalized KdV-Burgers equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:2 (2015), 253–266; Comput. Math. Math. Phys., 55:2 (2015), 251–263
A. T. Il'ichev, V. A. Shargatov, “Dynamics of water evaporation fronts”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1531–1553; Comput. Math. Math. Phys., 53:9 (2013), 1350–1370
S. A. Gubin, V. A. Shargatov, “Numerical simulation of changes in the composition of detonation products of a free volume of a combustible mixture”, Fizika Goreniya i Vzryva, 48:3 (2012), 46–52; Combustion, Explosion and Shock Waves, 48:3 (2012), 288–293
Yu. A. Gostintsev, S. A. Gubin, S. I. Sumskoi, V. A. Shargatov, “Numerical modeling of the detonation of a submerged hydrogen-air jet”, Fizika Goreniya i Vzryva, 26:4 (1990), 110–116; Combustion, Explosion and Shock Waves, 26:4 (1990), 473–478
S. A. Gubin, V. A. Shargatov, “Parameters of air shock waves when combustion is transformed into detonation”, Fizika Goreniya i Vzryva, 25:5 (1989), 111–115; Combustion, Explosion and Shock Waves, 25:5 (1989), 621–625
S. A. Gubin, V. A. Shargatov, “Self-similar processes in the propagation of a deflagration in an open volume under the assumption of an equilibrium composition of the combustion products”, Fizika Goreniya i Vzryva, 25:4 (1989), 44–53; Combustion, Explosion and Shock Waves, 25:4 (1989), 421–428
A. A. Borisov, B. E. Gel'fand, S. A. Gubin, S. I. Sumskoi, V. A. Shargatov, “Detonation of fuel-air mixtures above the surface of the Earth”, Fizika Goreniya i Vzryva, 24:2 (1988), 124–126; Combustion, Explosion and Shock Waves, 24:2 (1988), 238–240
B. E. Gel'fand, S. A. Gubin, V. N. Mikhalkin, V. A. Shargatov, “Calculation of the shock wave parameters from the detonation of combustible gas mixtures of variable composition”, Fizika Goreniya i Vzryva, 21:3 (1985), 92–97; Combustion, Explosion and Shock Waves, 21:3 (1985), 355–360
A. P. Voitov, B. E. Gel'fand, S. A. Gubin, V. N. Mikhalkin, V. A. Shargatov, “Effect of composition of a combustible gas mixture on the parameters of a plane shock wave generated by an explosion in air”, Fizika Goreniya i Vzryva, 20:1 (1984), 90–93; Combustion, Explosion and Shock Waves, 20:1 (1984), 82–84
S. A. Gubin, V. V. Odintsov, V. A. Shargatov, V. I. Pepekin, “On the calculation of the detonation rate of condensed explosives with solid products”, Dokl. Akad. Nauk SSSR, 261:3 (1981), 592–595
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