one-dimensional motions of continuous media,
stability of motions of continuous media,
magnetohydrodynamics,
elasticity theory.
Subject:
The main scientific interests are concerned with investigation of one-dimensional motions of continuous media, of stability of motions of continuous media, with various problems of magnetohydrodynamics, elasticity theory. In particular, these are: development of analytical methods and numerical simulation of nonlinear fenomena in various problems of mechanics of continuous media, concerned with stability of flows, propagation of wave fronts and shock waves of various structures in inhomogeneous and anisotropic media with dissipative and dispersive properties, interactions of nonlinear waves and shock waves as well as with influence of their structures on the properties of global solutions, including possible nonuniqueness of solutions. The main results are: theoretical investigation of the fronts of ionization and recombination in a gas with a magnetic field. It was found that these fronts possess fairly peculiar properties. For extended systems the instability conditions have been analyzed and there was introduced the concept of global instability as the instability which arises as a closed chain of waves growing with time and mutually transformung one to another. It was investigated also a behaviour of weakly nonlinear waves in a weakly anisotropic elastic medium. A nonuniqueness of solutions was found for typical selfsimilar problems. The similar problems have been studied numerically for viscous media. It was shown that for the case of nonuniqueness of solutions the asymptotic of the solution can be different and depending on the details which are vanishing when the viscousity is absent. The similar problem arose also for the case when dispersion also plays an essential role in the formation of structure of the shock wave, and this problem now is also under investigation.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov State University (MSU) in 1955 (Department of hydromechanics). PhD. thesis was defended in 1959 (Advisor: academician L. I. Sedov). Joined Mathematical Institute in 1958. D.Sci. thesis "On some generic properties of one-dimensional flows of continuous media" was defended in 1969. A list of my publications contains more than 120 paper titles. I, A. A. Barmin and V. P. Karlikov have led the research seminar at the Department of hydromechanics of Moscow State University.
In 1967 I was awarded the prize named after S. A. Chaplygin for investigation of flows stability in extended regions.
Main publications:
A. G. Kulikovskii, G. A. Lyubimov, Magnitnaya gidrodinamika, Fizmatgiz, M., 1962, 246 с.
A. G. Kulikovskii, E. I. Sveshnikova, Nelineinye volny v uprugikh sredakh, Izd-vo <<Moskovskii Litsei>>, M., 1998, 412 с.
A. G. Kulikovskii, “Silnye razryvy v techeniyakh sploshnykh sred i ikh struktura”, Tr. MIAN, 182, 1988, 261–291
A. G. Kulikovskii, A. P. Chugainova, “Klassicheskie i neklassicheskie razryvy v resheniyakh uravnenii nelineinoi teorii uprugosti”, UMN, 63:2(380) (2008), 85–152
A. G. Kulikovskii, “O mnogoparametricheskikh frontakh silnykh razryvov v mekhanike sploshnykh sred”, Prikladnaya matematika i mekhanika, 75:4 (2011), 531–550
A. G. Kulikovskii, “Note on the correspondence of solutions of some systems of equations”, Prikl. Mekh. Tekh. Fiz., 65:5 (2024), 112–116
2.
A. G. Kulikovskii, “Special discontinuities in solving the self-similar problem of waves in a rod”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024
2023
3.
A. G. Kulikovskii, A. P. Chugainova, “Longitudinal–Torsional Waves in Nonlinear Elastic Rods”, Proc. Steklov Inst. Math., 322 (2023), 151–160
4.
A. G. Kulikovskii, J. S. Zayko, “On Waves on the Surface of an Unstable Layer of a Viscous Fluid Flowing Down a Curved Surface”, Proc. Steklov Inst. Math., 322 (2023), 140–150
5.
A. P. Chugainova, A. G. Kulikovskii, “Structures of longitudinal-torsional shock waves and special discontinuities in nonlinearly viscoelastic media with dispersion”, Contin. Mech. Thermodyn., 35 (2023), 1655–1669;
A. G. Kulikovskii, A. P. Chugainova, “Structures of non-classical discontinuities in solutions of hyperbolic systems of equations”, Russian Math. Surveys, 77:1 (2022), 47–79
7.
A. Kulikovskii, J. Zayko, “Asymptotic behavior of localized disturbance in a viscous fluid flow down an incline”, Phys. Fluids, 34:3 (2022), 034119 ;
A. P. Chugainova, A. G. Kulikovskii, “Shock waves in an incompressible anisotropic elastoplastic medium with hardening and their structures”, Appl. Math. Comput., 401 (2021), 126077 , 11 pp. ;
A. G. Kulikovskii, A. P. Chugainova, “Discontinuity structures of equation solutionsdescribing longitudinal-torsional waves in elastic rods”, Doklady RAN. Fiz. Tekhn. Nauki, 497:1 (2021), 49–52
2020
10.
A. P. Chugainova, A. G. Kulikovskii, “Longitudinal and torsional shock waves in anisotropic elastic cylinders”, Z. Angew. Math. Phys., 71:1 (2020), 17 , 15 pp. ;
A. G. Kulikovskii, A. P. Chugainova, “Simple One-Dimensional Waves in an Incompressible Anisotropic Elastoplastic Medium with Hardening”, Proc. Steklov Inst. Math., 310 (2020), 175–184
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”, J. Exp. Theor. Phys., 131:3 (2020), 481–495
13.
Izbrannye voprosy matematiki i mekhaniki, Sbornik statei. K 70-letiyu so dnya rozhdeniya akademika Valeriya Vasilevicha Kozlova, Trudy MIAN, 310, ed. D. V. Treschev, S. V. Bolotin, A. G. Kulikovskii, I. A. Taimanov, MIAN, M., 2020 , 341 pp.
2019
14.
A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “Spontaneously radiating shock waves”, Doklady Physics, 64:7 (2019), 293–296
15.
A. G. Kulikovskii, N. A. Kulikovsky, N. T. Pashchenko, “On perturbations of a tangential discontinuity surface between two non-uniform flows of an ideal non-compressible fluid”, J. Appl. Mech. Tech. Phys., 60:2 (2019), 211–223
2018
16.
A. G. Kulikovskii, E. I. Sveshnikova, “Problem of the Motion of an Elastic Medium Formed at the Solidification Front”, Proc. Steklov Inst. Math., 300 (2018), 86–99
17.
A. G. Kulikovskii, A. P. Chugainova, “Shock Waves in Anisotropic Cylinders”, Proc. Steklov Inst. Math., 300 (2018), 100–113
18.
A. G. Kulikovskii, “Note on the Nature of Spontaneously Radiating Shock Waves”, Dokl. Math., 63:8 (2018), 334–336
19.
Sovremennye problemy i metody mekhaniki, Sbornik statei. K 110-letiyu so dnya rozhdeniya akademika Leonida Ivanovicha Sedova, Trudy MIAN, 300, ed. A. G. Kulikovskii, A. T. Ilichev, A. P. Chugainova, MAIK «Nauka/Interperiodika», M., 2018 , 239 pp.
2017
20.
A. G. Kulikovskii, E. I. Sveshnikova, “Fronty obrazovaniya nelineinoi uprugoi sredy iz sredy bez kasatelnykh napryazhenii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2017, no. 3, 48–54
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, “Evolution of perturbations on a steady weakly inhomogeneous background. Complex Hamiltonian equations”, J. Appl. Math. Mech., 81:1 (2017), 1–10
23.
A. G. Kulikovskii, A. P. Chugainova, “Long nonlinear waves in anisotropic cylinders”, Comput. Math. Math. Phys., 57:7 (2017), 1194–1200
2016
24.
A. G. Kulikovskii, A. P. Chugainova, “Study of discontinuities in solutions of the Prandtl-Reuss elastoplasticity equations”, Comput. Math. Math. Phys., 56:4 (2016), 637–649
25.
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”, Comput. Math. Math. Phys., 56:7 (2016), 1355–1362
26.
A. G. Kulikovskii, A. P. Chugainova, “A self-similar wave problem in a Prandtl–Reuss elastoplastic medium”, Proc. Steklov Inst. Math., 295 (2016), 179–189
27.
A. G. Kulikovskii, “Remarks on the paper by Sh. A. Mukhamediev, E. I. Ryzhak,and S. V. Sinyukhina “Stability of a two-layer system ofinhomogeneous heavy barotropic fluids”, J. Appl. Math. Mech.: 2016, Vol. 80, No. 3, pp. 264–270”, J. Appl. Math. Mech., 80:3 (2016), 271–272
2015
28.
A. G. Kulikovskii, A. P. Chugainova, “Shock Waves in Elastoplastic Media with the Structure Defined by the Stress Relaxation Process”, Proc. Steklov Inst. Math., 289 (2015), 167–182
29.
A. G. Kulikovskii, A. P. Chugainova, “Struktura uprugoplasticheskikh udarnykh voln”, KhI Vserossiiskii s'ezd po fundamentalnym problemam teoreticheskoi i prikladnoi mekhaniki, Kazan, 20–24 avgusta 2015 g., Kazanskii (Privolzhskii) federalnyi universitet, Kazan, 2015, 2173–2174
30.
A. G. Kulikovskii, E. I. Sveshnikova, “Anisotropic elastic medium formation in a compression front of particles flow”, J. Appl. Math. Mech., 79:6 (2015), 521–530
31.
V. N. Belykh, K. V. Brushlinskii, V. L. Vaskevich, S. P. Kiselev, A. N. Kraiko, A. G. Kulikovskii, V. I. Mali, V. V. Pukhnachov, E. I. Romensky, V. S. Ryaben'kii, “Sergei Konstantinovich Godunov has turned 85 years old”, Russian Math. Surveys, 70:3 (2015), 561–590
2014
32.
V. B. Demidovich, V. P. Dymnikov, G. M. Kobel'kov, V. V. Kozlov, A. G. Kulikovskii, V. A. Sadovnichii, V. M. Tikhomirov, E. E. Tyrtyshnikov, V. N. Chubarikov, M. È. Èglit, “Nikolai Sergeevich Bakhvalov (on his 80th birthday)”, Russian Math. Surveys, 69:3 (2014), 579–582
2013
33.
A. G. Kulikovskii, N. T. Pashchenko, “Stability of a Flame Front in a Divergent Flow”, Proc. Steklov Inst. Math., 281 (2013), 49–61
34.
“The overturning of Riemann waves in elastoplastic media with hardening”, J. Appl. Math. Mech., 77:4 (2013), 350–359
2012
35.
A. G. Kulikovskii, N. V. Pogorelov, A. Yu. Semenov, Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, izd. 2-e, ispravl. i dop., Fizmatlit, M., 2012 , 656 pp.
2011
36.
A. G. Kulikovskii, “Multi-parameter fronts of strong discontinuities in continuum mechanics”, J. Appl. Math. Mech., 75:4 (2011), 378–389
37.
A. G. Kulikovskii, E. I. Sveshnikova, “Near-resonace transverse oscillations in an elastic layer. Steady-state solutions”, J. Appl. Math. Mech., 75:1 (2011), 19–26
2010
38.
A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova, Matematicheskie metody izucheniya razryvnykh reshenii nelineinykh giperbolicheskikh sistem uravnenii, Lekts. kursy NOTs, 16, MIAN, M., 2010 , 122 pp.
A. G. Kulikovskii, A. P. Chugainova, “O statsionarnoi strukture udarnykh voln v uprugikh sredakh i dielektrikakh”, ZhETF, 137:5 (2010), 973–985
13
40.
A. G. Kulikovskii, A. P. Chugainova, “Self-similar asymptotics describing nonlinear waves in elastic media with dispersion and dissipation”, Comput. Math. Math. Phys., 50:12 (2010), 2145–2156
41.
A. G. Kulikovskii, N. T. Pashchenko, “The effect of a small background inhomogeneity on the asymptotic properties of linear perturbations”, J. Appl. Math. Mech., 74:2 (2010), 127–134
42.
A. G. Kulikovskii, E. I. Sveshnikova, “Transmission of oscillations through a layer of a nonlinear elastic medium”, Acoustical Physics, 56:6 (2010), 893–903
2009
43.
A. G. Kulikovskii, N. T. Paschenko, “Razvitie vozmuschenii na fone, blizkom k odnorodnomu, v sluchae neustoichivisti”, Trudy konferentsii «Sovremennye problemy mekhaniki sploshnoi sredy», posvyaschennoi pamyati akademika L. I. Sedova v svyazi so stoletiem so dnya ego rozhdeniya, Torrus press, M., 2009, 208–225
44.
A. G. Kulikovskii, N. T. Paschenko, “Ustoichivost fronta plameni v raskhodyaschemsya potoke”, Sb. nauchnykh trudov «Uspekhi mekhaniki sploshnykh sred» k 70-letiyu akademika V. A. Levina, Dalnauka, Vladivostok, 2009, 365–381
45.
A. G. Kulikovskii, E. I. Sveshnikova, “Nelineinye volny v uprugikh sredakh. Needinstvennost reshenii”, Cb. «Sovremennye problemy matematiki, mekhaniki i ikh prilozheniya», posvyaschennyi 70-letiyu V. A. Sadovnichego, Izd-vo Mosk. un-ta, M., 2009, 58–65
46.
A. G. Kulikovskii, A. P. Chugainova, “On solution non-uniqueness in the nonlinear elasticity theory”, Reviews on Advanced Materials Science, 19:1/2 (2009), 93–98
2008
47.
A. G. Kulikovskii, Ye. I. Sveshnikova, “A model for describing near-resonance oscillations in an elastic layer”, J. Appl. Math. Mech., 72:6 (2008), 715–723
48.
A. G. Kulikovskii, E. I. Sveshnikova, “Okolorezonansnye kolebaniya sloya neszhimaemoi uprugoi sredy”, Problemy sovremennoi mekhaniki, Izd-vo MGU, Izd-vo Omega-L, M., 2008, 207–221
49.
A. G. Kulikovskii, N. T. Paschenko, “O razvitii vozmuschenii na fone, blizkom k odnorodnomu, v sluchae neustoichivisti”, Lomonosovskie chteniya, Tezisy dokladov nauchnoi konferentsii. Sektsiya mekhaniki (Aprel 2008, Moskva, MGU imeni M. V. Lomonosova), Izd-vo Mosk. un-ta, M., 2008, 115
50.
A. G. Kulikovskii, A. P. Chugainova, “The influence of small scale dispersion and dissipation on nonlinear waves in elastic media”, The problem of solution non-uniqueness in hyperbolic approximation, Proceedings of XXXVI International Summer School-Conference “Advanced Problems in Mechanics” APM'2008 (St. Petersburg, Repino, Jule 6 – Jule 10, 2008), 2008, 394–400
51.
A. G. Kulikovskii, A. P. Chugainova, “Classical and non-classical discontinuities in solutions of equations of non-linear elasticity theory”, Russian Math. Surveys, 63:2 (2008), 283–350
52.
A. G. Kulikovskii, E. I. Sveshnikova, “Opisanie evolyutsii okolorezonansnykh kolebanii sloya uprugoi sredy”, Trudy VIII Vserossiiskoi nauchnoi konferentsii «Nelineinye kolebaniya mekhanicheskikh sistem», Nizhnii Novgorod, 2008, 30–34
2007
53.
A. G. Kulikovskii, A. V. Lozovskii, N. T. Pashchenko, “On the development of perturbations on a weakly inhomogeneous background”, J. Appl. Math. Mech., 71:5 (2007), 690–700
2012
54.
A. G. Kulikovskii and A. P. Chugainova, “Classical and nonclassical discontinuities and their structures in nonlinear elastic media with dispersion and dissipation”, Proceedings of the Steklov Institute of Mathematics, 276, Suppl. 2 (2012), 1–68
2006
55.
A. G. Kulikovskii, E. I. Sveshnikova, “Nonlinear near-resonance oscillations of a layer of an elastic incompressible medium”, J. Appl. Math. Mech., 70:6 (2006), 924–933
56.
A. G. Kulikovskii, A. P. Chugainova, E. I. Sveshnikova, “On the nonuniqueness of solutions to the nonlinear equations of elasticity theory”, J. Engrg. Math., 55:1-4 (2006), 97–110
A. G. Kulikovskiĭ, “On the global instability of homogeneous flows in non-one-dimensional domains”, J. Appl. Math. Mech., 70:2 (2006), 229–234
2005
58.
A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova, “Some Problems in Nonlinear Dynamic Elasticity”, Proc. Steklov Inst. Math., 251 (2005), 165–191
59.
A. G. Kulikovskii, N. T. Pashchenko, “Propagation regimes of self-supported light-detonation waves”, Fluid Dynam., 40:5 (2005), 818–828
60.
A. G. Kulikovskii, G. A. Lyubimovym, Magnitnaya gidrodinamika, Logos, M., 2005 , 325 pp.
2004
61.
A. G. Kulikovskii, A. P. Chugainova, “Modeling the influence of small-scale dispersion processes in a continuum on the formation of large-scale phenomena”, Comput. Math. Math. Phys., 44:6 (2004), 1062–1068
62.
A. G. Kulikovskii, “Phase transitions in flow through a heat-conducting porous skeleton”, Fluid Dynam., 39:3 (2004), 429–434
2003
63.
A. G. Kulikovskii, E. I. Sveshnikova, “The effect of a change in entropy on the shape of the shock adiabatic curve of quasitransverse elastic waves”, J. Appl. Math. Mech., 67:1 (2003), 79–88
2002
64.
A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova, “On nonuniqueness of solutions in the nonlinear theory of elasticity”, Modeli mekhaniki sploshnoi sredy, Obzornye doklady i lektsii XVI sessii mezhd. shkoly po modelyam mekhaniki sploshnoi sredy (Kazan, 2002), Tr. Matem. tsentra im. N. I. Lobachevskogo, 16, Izd-vo Kazan. matem. ob-va, Kazan, 2002, 6–25
65.
A. G. Kulikovskii, A. P. Chugainova, “Ob ustoichivosti k dvumernym vozmuscheniyam metastabilnoi udarnoi volny v vyazkouprugoi srede”, PMM, 66:1 (2002), 109–117
6
66.
A. G. Kulikovskii, “Evaporation and condensation fronts in porous media”, Fluid Dynam., 37:5 (2002), 740–746
2001
67.
A. G. Kulikovskii, N. V. Pogorelov, A. Yu. Semenov, Mathematical aspects of numerical solution of hyperbolic systems, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 118, Chapman & Hall/CRC, Boca Raton, FL, 2001 , xiv+540 pp.
68.
A. G. Kulikovskiĭ, N. V. Pogorelov, A. Yu. Semenov, Mathematical problems in the numerical solution of hyperbolic systems of equations, Fiziko-Matematicheskaya Literatura, Moscow, 2001 , 608 pp.
69.
A. G. Kulikovskiĭ, E. I. Sveshnikova, “A condition for the nonexistence and nonuniqueness of solutions of self-similar problems of continuum mechanics”, J. Appl. Math. Mech., 65:6 (2001), 941–950 (2002)
2000
70.
A. G. Kulikovskii, A. P. Chugainova, “Ob ustoichivosti kvazipoperechnykh udarnykh voln v anizotropnykh uprugikh sredakh”, PMM, 64:6 (2000), 1020–1026
4
71.
A. G. Kulikovskii, I. S. Shikina, “Conditions of instability of a flame front in a weakly inhomogeneous flow”, Fluid Dynam., 35:5 (2000), 635–641
72.
N. I. Gvozdovskaya, A. G. Kulikovskii, “Peculiar structure of the set of admissible discontinuities in problems with dispersion”, Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000), SIAM, Philadelphia, PA, 2000, 158–162
73.
A. G. Kulikovskii, G. A. Lyubimov, “Leonid Ivanovich Sedov (obituary)”, Russian Math. Surveys, 55:2 (2000), 323–326
1999
74.
A. G. Kulikovskii, N. V. Pogorelov, A. Yu. Semenov, “Mathematical aspects of numerical solution of hyperbolic systems”, Hyperbolic problems: theory, numerics, applications (Zürich, 1998), v. II, Internat. Ser. Numer. Math., 130, Birkhäuser, Basel, 1999, 589–598
75.
N. I. Gvozdovskaya, A. G. Kulikovskii, “Quasitransverse shock waves in elastic media with an internal structure”, J. Appl. Mech. Tech. Phys., 40:2 (1999), 341–346
76.
N. I. Gvozdovskaya, A. G. Kulikovskii, “Investigation of electromagnetic shock-wave structure in anisotropic ferromagnets with easy axis”, Wave Motion, 29:1 (1999), 23–34
N. I. Gvozdovskaya, A. G. Kulikovskii, “Quasitransverse shock waves in elastic media with an internal structure”, J. Appl. Mech. Tech. Phys., 40:2 (1999), 341–346
1998
78.
A. G. Kulikovskii, A. P. Chugainova, “Disintegration conditions for a nonlinear wave in a viscoelastic medium”, Comput. Math. Math. Phys., 38:2 (1998), 305–312
79.
A. G. Kulikovskii, N. I. Gvozdovskaya, “The Effect of Dispersion on the Set of Admissible Discontinuities in Continuum Mechanics”, Proc. Steklov Inst. Math., 223 (1998), 55–65
80.
A. G. Kulikovskii, E. I. Sveshnikova, Nelineinye volny v uprugikh sredakh, Moskovskii litsei, M., 1998 , 412 pp.
1997
81.
N. I. Gvozdovskaya, A. G. Kulikovskii, “Electromagnetic shock waves and their structure in anisotropic magnets”, J. Appl. Math. Mech., 61:1 (1997), 135–143
82.
A. G. Kulikovskij, I. S. Shikina, “Influence of viscosity on stability of tangential discontinuity in incompressible liquid”, Mosc. Univ. Mech. Bull., 52:6 (1997), 6–9
1996
83.
M. E. Eglit, A. N. Golubiatnikov, J. A. Kamenjarzh, V. P. Karlikov, A. G. Kulikovsky, A. G. Petrov, I. S. Shikina, E. I. Sveshnikova, Continuum mechanics via problems and exercises. Part II: Answers and solutions, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 19, World Scientific Publishing Co. Inc., River Edge, NJ, 1996 , xii+253 pp.
M. E. Eglit, A. N. Golubiatnikov, J. A. Kamenjarzh, V. P. Karlikov, A. G. Kulikovsky, A. G. Petrov, I. S. Shikina, E. I. Sveshnikova, Continuum mechanics via problems and exercises. Part I: Theory and problems, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 19, World Scientific Publishing Co. Inc., River Edge, NJ, 1996 , xiv+270 pp.
M. A. Brutyan, A. G. Kulikovskii, “Instability and nonuniqueness of quasisteady flows of a viscoelastic liquid”, Fluid Dynam., 31:6 (1996), 819–827 (1997)
86.
A. G. Kulikovskii, I. S. Shikina, “On the transition to instability in weakly inhomogeneous flows without dissipation”, J. Appl. Math. Mech., 60:3 (1996), 429–432
87.
Yu. A. Drozdova, A. G. Kulikovskii, “Concerning the description of long nonlinear waves in channels”, Fluid Dynam., 31:5 (1996), 739–746 (1997)
88.
A. G. Kulikovskiĭ, E. I. Sveshnikova, “On the existence and uniqueness of self-similar solutions when there are Jouguet points on the shock adiabat”, J. Appl. Math. Mech., 60:1 (1996), 61–65
89.
A. A. Barmin, A. G. Kulikovskiy, N. V. Pogorelov, “Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics”, J. Comput. Phys., 126:1 (1996), 77–90
N. I. Gvozdovskaya, A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova, “Nonlinear waves in solids”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 6, 12–15
1995
91.
A. Kulikovskii, E. Sveshnikova, Nonlinear waves in elastic media, CRC Press, Boca Raton, FL, 1995 , x+237 pp.
92.
A. G. Kulikovskii, “The effect of small anisotropy on the properties of shock waves in a compressible elastic medium”, J. Appl. Math. Mech., 59:5 (1995), 763–767
93.
A. G. Kulikovskii, “Small amplitude nonlinear waves in an anisotropic elastic body”, Proc. Steklov Inst. Math., 211 (1995), 262–274
1993
94.
A. G. Kulikovskii, “On the stability loss of weakly non-uniform flows in extended regions. The formation of transverse oscillations of a tube conveying a fluid”, J. Appl. Math. Mech., 57:5 (1993), 851–856 (1994)
95.
A. G. Kulikovskii, E. I. Sveshnikova, “Riemann waves in an elastic medium with small anisotropy”, J. Appl. Math. Mech., 57:3 (1993), 493–502
1992
96.
S. A. Egorushkin, A. G. Kulikovskii, “Stability of solutions of some boundary value problems for hyperbolic equations”, J. Appl. Math. Mech., 56:1 (1992), 36–45
1990
97.
A. G. Kulikovskii, L. A. Pekurovskaya, “Longitudinal waves in an elastic medium with piecewise linear dependence of the stress on deformation”, J. Appl. Math. Mech., 54:5 (1990), 663–668 (1991)
1989
98.
A. G. Kulikovskii, L. A. Pekurovskaya, “Fronts of strong and weak discontinuity in solutions of equations in polymodular elasticity theory”, J. Appl. Math. Mech., 53:2 (1989), 230–235 (1990)
99.
A. G. Kulikovskii, “Peculiarities of the behavior of nonlinear quasitransversal waves in an elastic medium with a small anisotropy”, Current mathematical problems in mechanics and their applications, Dedicated to Academician L. I. Sedov on his 80th birthday, Trudy Mat. Inst. Steklov., 186, Nauka, Moscow, 1989, 132–139
1988
100.
A. G. Kulikovskii, E. I. Sveshnikova, “On the decay of an arbitrary initial discontinuity in an elastic medium”, J. Appl. Math. Mech., 52:6 (1988), 786–790 (1990)
1990
101.
A. G. Kulikovskii, “Strong discontinuities in flows of continua and their structure”, Proc. Steklov Inst. Math., 182 (1990), 285–317
1987
102.
A. G. Kulikovskiĭ, E. I. Sveshnikova, “On the structure of quasitransverse elastic shock waves”, J. Appl. Math. Mech., 51:6 (1987), 711–716 (1989)
1986
103.
A. G. Kulikovskii, “Equations describing the propagation of non-linear quasitransverse waves in a weakly non-isotropic elastic body”, J. Appl. Math. Mech., 50:4 (1986), 455–461
104.
A. G. Kulikovskii, “Some comments on the book Hydrodynamics by L. D. Landau and E. M. Lifshits [Theoretical physics, Vol. VI, “Nauka”, Moscow, 1986]”, J. Appl. Math. Mech., 50:6 (1986), 806–807 (1987)
1985
105.
A. G. Kulikovskii, “On the stability conditions for stationary states or flows in regions extended in one direction”, J. Appl. Math. Mech., 49:3 (1985), 316–321
106.
A. A. Barmin, A. P. Glinov, A. G. Kulikovskii, “Occurrence of periodic regimes in steady supersonic MHD flows due to loss of electrical conductivity of medium”, Fluid Dynam., 20:4 (1985), 613–623
107.
A. G. Kulikovskii, I. S. Shikina, “On the asymptotic behavior of localized perturbations in the presence of Kelvin-Helmholtz instability”, Fluid Dynam., 20:2 (1985), 186–193
108.
A. G. Kulikovskii, E. I. Sveshnikova, “A self-similar problem on the action of a sudden load on the boundary of an elastic half-space”, J. Appl. Math. Mech., 49:2 (1985), 214–220 (1986)
109.
A. G. Kulikovskii, M. È. Èglit, “On a macroscopic method of entropy determination for non equilibrium states”, Dokl. Akad. Nauk SSSR, 284:1 (1985), 70–72
1984
110.
A. G. Kulikovskii, F. A. Slobodkina, “On the stability of one-dimensional stationary solutions of hyperbolic systems of differential equations containing points at which one characteristic velocity becomes zero”, J. Appl. Math. Mech., 48:3 (1984), 299–302 (1985)
111.
A. G. Kulikovskii, “The possible effect of oscillations in a discontinuity structure on the set of admissible discontinuities”, Soviet Phys. Dokl., 29:4 (1984), 283–285
112.
A. G. Kulikovskii, E. I. Sveshnikova, “Some properties of the shock adiabat of quasitransverse elastic waves”, J. Appl. Math. Mech., 48:5 (1984), 575–578
113.
A. G. Kulikovskii, “The possible effect of oscillations in a discontinuity structure on the set of admissible discontinuities”, Dokl. Akad. Nauk SSSR, 275:6 (1984), 1349–1352
1983
114.
G. G. Chernyĭ, A. G. Kulikovskiĭ, “Mechanics of fluids and gases”, Outlines of the development of mathematics in the USSR, “Naukova Dumka”, Kiev, 1983, 597–613
1982
115.
A. G. Kulikovskii, E. I. Sveshnikova, “Investigation of the shock adiabat of quasitransverse shock waves in a prestressed elastic medium”, J. Appl. Math. Mech., 46:5 (1982), 667–673
1981
116.
A. G. Kulikovskii, G. Ya. Galin, “Stability of one-dimensional gas flows in expanding regions”, Fluid Dynam., 16:2 (1981), 246–252
1980
117.
A. G. Kulikovskii, E. I. Sveshnikova, “On shock wave propagation in stressed isotropic nonlinearly elastic media”, J. Appl. Math. Mech., 44:3 (1980), 367–374 (1981)
1979
118.
A. G. Kulikovskii, “Properties of shock adiabats in the neighborhood of Jouguet points”, Fluid Dynam., 14:2 (1979), 317–320
1978
119.
A. A. Barmin, A. G. Kulikovskii, “Conditions for discontinuities and discontinuous flows of a conducting gas in an electromagnetic field”, Current problems in theoretical and applied mechanics, Proc. Fourth All-Union Congress Theoret. Appl. Mech. (Kiev, 1976), “Naukova Dumka”, Kiev, 1978, 199–216
1979
120.
A. A. Barmin, A. G. Kulikovskiy, “Discontinuous solutions in mechanics of continua”, Fluid Mech.—Soviet Res., 8:6 (1979), 75–95 (1980)
1977
121.
V. A. Kondrashev, A. G. Kulikovskii, “On boundaries of the growth region of multidimensional perturbations of unstable states”, J. Appl. Math. Mech., 41:6 (1977), 1141–1142
1975
122.
A. A. Barmin, A. G. Kulikovskii, “Piston problem in the presence of recombination waves in a magnetic field”, Fluid Dynam., 10:4 (1975), 653–658
123.
G. Ia. Galin, A. G. Kulikovskii, “On the stability of flows appearing at the disintegration of an arbitrary discontinuity”, J. Appl. Math. Mech., 39:1 (1975), 85–92
1974
124.
A. G. Kulikovskii, F. A. Slobodkina, “Choice of a self-similar solution in boundary-layer theory”, Fluid Dynam., 9:4 (1974), 536–539
1973
125.
A. G. Kulikovskii, “Flows of a conducting incompressible liquid in an arbitrary region with a strong magnetic field”, Fluid Dynam., 8:3 (1973), 462–467
126.
A. G. Kulikovskii, M. È. Èglit, “Two-dimensional problem of the motion of a snow avalanche along a slope with smoothly changing properties”, J. Appl. Math. Mech., 37:5 (1973), 792–803
1971
127.
A. A. Barmin, A. G. Kulikovskii, “Fronty ionizatsii i rekombinatsii v elektromagnitnom pole”, Itogi nauki. Gidrodinamika, 5, VINITI, M., 1971, 5–31
128.
A. G. Kulikovskiy, “On the stability of steady flows independent of a spatial coordinate”, Actes du Congrès International des Mathématiciens (Nice, 1970), Gauthier-Villars, Paris, 1971, 131–135
129.
V. B. Baranov, K. V. Krasnobaev, A. G. Kulikovskii, “A model of the interaction of the solar wind with the interstellar medium”, Soviet Phys. Dokl., 15 (1971), 791–793
1968
130.
A. G. Kulikovskii, F. A. Slobodkina, “Equilibrium of arbitrary steady flows at the transonic points”, J. Appl. Math. Mech., 31 (1968), 623–630
131.
A. G. Kulikovskii, “O poverkhnostyakh razryva, razdelyayuschikh idealnye sredy s razlichnymi svoistvami. Volny rekombinatsii”, PMM, 32:6 (1968), 1125–1131
132.
A. A. Barmin, A. G. Kulikovskii, “Ob udarnykh volnakh, ionizuyuschikh gaz, nakhodyaschikhsya v elektromagnitnom pole”, Dokl. AN SSSR, 178:1 (1968), 55–58
A. G. Kulikovskii, S. A. Regirer, “Influence of the walls on overheating instability in a magnetohyduodynamic channel”, J. Appl. Mech. Tech. Phys., 6:5 (1965), 22–25
1964
134.
S. V. Iordanskii, A. G. Kulikovskii, “A quasilinear approximation and the correlation functions for a plasma”, Soviet Physics JETP, 19 (1964), 499–506
135.
S. V. Iordanskii, A. G. Kulikovskii, “A general stability condition for higher correlation functions in a plasma”, Soviet Phys. Dokl., 9 (1964), 347–349
1963
136.
S. V. Iordanskii, A. G. Kulikovskii, “Stability of the higher correlation functions in a plasma”, Dokl. AN SSSR, 152 (1963), 849–852
1962
137.
A. G. Kulikovskii, “On the structure of shock waves in magnetohydrodynamics with arbitrary dissipation law”, J. Appl. Math. Mech., 26 (1962), 392–400
138.
A. G. Kulikovskii, “The structure of shock waves”, J. Appl. Math. Mech., 26 (1962), 950–964
1961
139.
A. G. Kulikovskii, G. A. Liubimov, “On the structure of an inclined magnetohydrodynamic shock wave”, J. Appl. Math. Mech., 25 (1961), 171–179
140.
A. G. Kulikovskii, “On the structure of slow magnetohydrodynamic shock waves in the barotropic case”, Sov. Phys. Dokl., 6 (1961), 302–304
1960
141.
A. G. Kulikovskii, G. A. Lyubimov, “On gas-ionizing magnetohydrodynamic shock waves”, Rev. Mod. Phys., 32 (1960), 977–979
A. G. Kulikovskij, G. A. Lyubimov, “Some remarks on the structure of a normal magneto-hydrodynamic shock wave”, J. Appl. Math. Mech., 23:6 (1959), 1644–1647
1960
143.
A. G. Kulikovskij, G. A. Lyubimov, “The simplest problems concerning gas-ionizing shock waves in an electromagnetic field”, Sov. Phys. Dokl., 4 (1960), 1195–1198
144.
A. G. Kulikovskii, G. A. Lyubimov, “Gas-ionizing magnetohydrodynamic shock waves”, Sov. Phys. Dokl., 4 (1960), 1185–1188
1958
145.
A. G. Kulikovskii, “On media in which unidimensional motions with homogeneous deformations are possible”, Dokl. AN SSSR, 120 (1958), 485–486
1959
146.
A. G. Kulikovskij, “On motions with homogenous deformation in magneto-hydrodynamics”, Sov. Phys. Dokl., 3 (1959), 507–509
1958
147.
A. G. Kulikovskii, “O volnakh Rimana v magnitnoi gidrodinamike”, Dokl. AN SSSR, 121 (1958), 987–990
Opening Speech A. G. Kulikovskii School for Young Mechanicians and Mathematicians “Mathematical Methods of Mechanics” November 10, 2020 10:45
7.
Spontaneously radiating shock wave structure stability A. G. Kulikovskii International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday January 20, 2020 15:00
Фронты затвердевания, задача о поршне A. G. Kulikovskii, E. I. Sveshnikova All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov November 14, 2017 17:20
Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, ed. D. V. Treschev, S. V. Bolotin, A. G. Kulikovskii, I. A. Taimanov, 2020, 341 с. http://mi.mathnet.ru/book1805
Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, ed. A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, 2018, 239 с. http://mi.mathnet.ru/book1686
A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova, Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations, Lekts. Kursy NOC, 16, 2010, 122 с. http://mi.mathnet.ru/book1249
A. G. Kulikovskii, A. P. Chugainova, Classical and Nonclassical Discontinuities and Their Structure in Nonlinear Elastic Media with Dispersion and Dissipation, Sovrem. Probl. Mat., 7, 2007, 150 с. http://mi.mathnet.ru/book470
2024
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