Kulikovskii, Andrey Gennadievich

Total publications: 143 (136)
in MathSciNet: 105 (102)
in zbMATH: 77 (74)
in Web of Science: 62 (58)
in Scopus: 80 (78)
Cited articles: 87
Citations in Math-Net.Ru: 124
Citations in MathSciNet: 165
Citations in Web of Science: 153
Citations in Scopus: 440
Presentations: 16

Number of views:
This page:7679
Abstract pages:9135
Full texts:3259
Kulikovskii, Andrey Gennadievich
Member of the Russian Academy of Sciences
Doctor of physico-mathematical sciences (1970)
Speciality: 01.02.05 (Mechanics of fluids, gases and plasmas)
Keywords: one-dimensional motions of continuous media, stability of motions of continuous media, magnetohydrodynamics, elasticity theory.


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.


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:
  1. A. G. Kulikovskii, G. A. Lyubimov, Magnitnaya gidrodinamika, Fizmatgiz, M., 1962, 246 с.
  2. A. G. Kulikovskii, E. I. Sveshnikova, Nelineinye volny v uprugikh sredakh, Izd-vo <<Moskovskii Litsei>>, M., 1998, 412 с.
  3. A. G. Kulikovskii, “Silnye razryvy v techeniyakh sploshnykh sred i ikh struktura”, Tr. MIAN, 182, 1988, 261–291  mathnet  mathscinet  zmath
  4. A. G. Kulikovskii, A. P. Chugainova, “Klassicheskie i neklassicheskie razryvy v resheniyakh uravnenii nelineinoi teorii uprugosti”, UMN, 63:2(380) (2008), 85–152  mathnet  mathscinet  zmath
  5. A. G. Kulikovskii, “O mnogoparametricheskikh frontakh silnykh razryvov v mekhanike sploshnykh sred”, Prikladnaya matematika i mekhanika, 75:4 (2011), 531–550
List of publications on Google Scholar

Full list of scientific publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. A. G. Kulikovskii, A. P. Chugainova, Uspekhi Mat. Nauk (to appear)  mathnet

2. 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.  mathnet  crossref  mathscinet  isi  scopus;  mathscinet
3. 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  mathnet  crossref  elib

4. 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.  mathnet  crossref  mathscinet  zmath  isi  scopus;  zmath
5. 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  mathnet  crossref  crossref  mathscinet  isi  elib  scopus (cited: 1)
6. 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  mathnet  crossref  crossref  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
7. 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.  mathnet

8. A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “Spontaneously radiating shock waves”, Doklady Physics, 64:7 (2019), 293–296  mathnet  crossref  crossref  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
9. Kulikovskii A.G., Kulikovskii N.A., Paschenko N.T., “Razvitie vozmuschenii poverkhnosti tangentsialnogo razryva mezhdu neodnorodnymi potokami idealnoi neszhimaemoi zhidkosti”, Prikladnaya mekhanika i tekhnicheskaya fizika, 60:2(354) (2019), 32-46  mathnet  crossref  mathscinet  zmath  isi  elib
10. A. G. Kulikovskii, “Matematicheskie modeli mekhaniki”, Matematicheskaya sostavlyayuschaya, 2-e izd., rassh. i dop., eds. N. N. Andreev, S. P. Konovalov, N. M. Panyunin, Matematicheskie etyudy, M., 2019, 28

11. 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  mathnet  crossref  crossref  mathscinet  isi  elib  scopus (cited: 1)
12. A. G. Kulikovskii, A. P. Chugainova, “Shock Waves in Anisotropic Cylinders”, Proc. Steklov Inst. Math., 300 (2018), 100–113  mathnet  crossref  crossref  mathscinet  isi  elib  scopus (cited: 1)
13. A. G. Kulikovskii, “Note on the Nature of Spontaneously Radiating Shock Waves”, Dokl. Math., 63:8 (2018), 334–336  mathnet  crossref  crossref  isi  elib  scopus (cited: 3)
14. 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.  mathnet

15. 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  mathnet (cited: 1)  isi
16. 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.  mathnet  crossref  mathscinet  isi (cited: 12)  scopus (cited: 12)
17. A. G. Kulikovskii, “Evolution of perturbations on a steady weakly inhomogeneous background. Complex Hamiltonian equations”, J. Appl. Math. Mech., 81:1 (2017), 1–10  mathnet  crossref  mathscinet  mathscinet  isi  elib  elib  scopus (cited: 1)
18. A. G. Kulikovskii, A. P. Chugainova, “Long nonlinear waves in anisotropic cylinders”, Comput. Math. Math. Phys., 57:7 (2017), 1194–1200  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus (cited: 2)

19. 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  mathnet  crossref  crossref  mathscinet  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 6)
20. 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  mathnet  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus (cited: 9)
21. 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  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus (cited: 3)
22. 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  mathnet  crossref  mathscinet  isi  elib  elib  scopus

23. 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  mathnet  crossref  crossref  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 4)
24. 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  elib
25. 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  mathnet  crossref  isi  elib  elib  scopus (cited: 2)
26. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus

27. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

28. A. G. Kulikovskii, N. T. Pashchenko, “Stability of a Flame Front in a Divergent Flow”, Proc. Steklov Inst. Math., 281 (2013), 49–61  mathnet  crossref  crossref  mathscinet  isi  elib
29. “The overturning of Riemann waves in elastoplastic media with hardening”, J. Appl. Math. Mech., 77:4 (2013), 350–359  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 5)

30. 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.  mathscinet

31. A. G. Kulikovskii, “Multi-parameter fronts of strong discontinuities in continuum mechanics”, J. Appl. Math. Mech., 75:4 (2011), 378–389  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus (cited: 5)
32. 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  crossref  mathscinet  isi  elib  scopus

33. 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.  mathnet  mathnet (cited: 3)  crossref  zmath  elib
34. A. G. Kulikovskii, A. P. Chugainova, “O statsionarnoi strukture udarnykh voln v uprugikh sredakh i dielektrikakh”, ZhETF, 137:5 (2010), 973–985  elib (cited: 5)
35. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib  elib  scopus (cited: 4)
36. 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  crossref  mathscinet  zmath  isi  elib  elib  scopus
37. A. G. Kulikovskii, E. I. Sveshnikova, “Transmission of oscillations through a layer of a nonlinear elastic medium”, Acoustical Physics, 56:6 (2010), 893–903  crossref  adsnasa  isi

38. 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
39. 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
40. 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
41. 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  isi  elib

42. 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  crossref  mathscinet  isi  elib  scopus (cited: 1)
43. 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
44. 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
45. 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
46. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 6)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 18)
47. 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

48. 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  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 2)

49. 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  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 1)

50. 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  crossref  mathscinet  isi  elib  elib  scopus (cited: 1)
51. 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  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 6)  scopus (cited: 3)
52. A. G. Kulikovskiĭ, “On the global instability of homogeneous flows in non-one-dimensional domains”, J. Appl. Math. Mech., 70:2 (2006), 229–234  crossref  mathscinet  zmath  isi (cited: 7)  elib  scopus (cited: 8)

53. A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova, “Some Problems in Nonlinear Dynamic Elasticity”, Proc. Steklov Inst. Math., 251 (2005), 165–191  mathnet  mathscinet  zmath
54. A. G. Kulikovskii, N. T. Pashchenko, “Propagation regimes of self-supported light-detonation waves”, Fluid Dynam., 40:5 (2005), 818–828  crossref  mathscinet  zmath  adsnasa  scopus (cited: 8)
55. A. G. Kulikovskii, G. A. Lyubimovym, Magnitnaya gidrodinamika, Logos, M., 2005 , 325 pp.

56. 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  mathnet  mathscinet  zmath  scopus (cited: 16)
57. A. G. Kulikovskii, “Phase transitions in flow through a heat-conducting porous skeleton”, Fluid Dynam., 39:3 (2004), 429–434  crossref  mathscinet  zmath  adsnasa  scopus (cited: 4)

58. 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  crossref  mathscinet  zmath  isi  scopus

59. 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  mathscinet
60. A. G. Kulikovskii, A. P. Chugainova, “Ob ustoichivosti k dvumernym vozmuscheniyam metastabilnoi udarnoi volny v vyazkouprugoi srede”, PMM, 66:1 (2002), 109–117  zmath
61. A. G. Kulikovskii, “Evaporation and condensation fronts in porous media”, Fluid Dynam., 37:5 (2002), 740–746  crossref  mathscinet  zmath  isi (cited: 11)

62. 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.  mathscinet  zmath
63. 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.  mathscinet  zmath
64. 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)  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 3)

65. A. G. Kulikovskii, A. P. Chugainova, “Ob ustoichivosti kvazipoperechnykh udarnykh voln v anizotropnykh uprugikh sredakh”, PMM, 64:6 (2000), 1020–1026  mathscinet  zmath
66. 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  crossref  mathscinet  zmath  elib
67. 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  mathscinet  zmath
68. A. G. Kulikovskii, G. A. Lyubimov, “Leonid Ivanovich Sedov (obituary)”, Russian Math. Surveys, 55:2 (2000), 323–326  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi

69. 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  mathscinet  zmath  isi (cited: 10)
70. 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  crossref  mathscinet  zmath  adsnasa
71. 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  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 4)  scopus (cited: 5)

72. 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  mathnet  mathscinet  zmath  scopus (cited: 52)
73. 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  mathnet  mathscinet  zmath
74. A. G. Kulikovskii, E. I. Sveshnikova, Nelineinye volny v uprugikh sredakh, Moskovskii litsei, M., 1998 , 412 pp.

75. N. I. Gvozdovskaya, A. G. Kulikovskii, “Electromagnetic shock waves and their structure in anisotropic magnets”, J. Appl. Math. Mech., 61:1 (1997), 135–143  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 4)
76. 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  mathnet  mathscinet  zmath  isi

77. 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.  crossref  mathscinet  zmath
78. 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.  crossref  mathscinet  zmath
79. M. A. Brutyan, A. G. Kulikovskii, “Instability and nonuniqueness of quasisteady flows of a viscoelastic liquid”, Fluid Dynam., 31:6 (1996), 819–827 (1997)  crossref  mathscinet  zmath  adsnasa  scopus (cited: 3)
80. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
81. Yu. A. Drozdova, A. G. Kulikovskii, “Concerning the description of long nonlinear waves in channels”, Fluid Dynam., 31:5 (1996), 739–746 (1997)  crossref  mathscinet  zmath  adsnasa  scopus
82. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
83. 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  crossref  mathscinet  zmath  adsnasa  isi (cited: 67)  elib (cited: 75)  scopus (cited: 80)
84. 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  mathnet  zmath

85. A. Kulikovskii, E. Sveshnikova, Nonlinear waves in elastic media, CRC Press, Boca Raton, FL, 1995 , x+237 pp.  mathscinet  zmath
86. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)
87. A. G. Kulikovskii, “Small amplitude nonlinear waves in an anisotropic elastic body”, Proc. Steklov Inst. Math., 211 (1995), 262–274  mathnet  mathscinet  zmath

88. 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)  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
89. A. G. Kulikovskii, E. I. Sveshnikova, “Riemann waves in an elastic medium with small anisotropy”, J. Appl. Math. Mech., 57:3 (1993), 493–502  crossref  mathscinet  zmath  isi  scopus (cited: 1)

90. 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  crossref  mathscinet  zmath  isi  scopus (cited: 1)

91. 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)  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2)

92. 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)  crossref  mathscinet  zmath  isi  scopus (cited: 1)
93. 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  mathnet  mathscinet  zmath

94. 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)  crossref  mathscinet  zmath  isi  scopus (cited: 3)

95. A. G. Kulikovskii, “Strong discontinuities in flows of continua and their structure”, Proc. Steklov Inst. Math., 182 (1990), 285–317  mathnet  mathscinet  zmath

96. A. G. Kulikovskiĭ, E. I. Sveshnikova, “On the structure of quasitransverse elastic shock waves”, J. Appl. Math. Mech., 51:6 (1987), 711–716 (1989)  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 9)

97. 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  crossref  mathscinet  zmath  scopus (cited: 13)
98. 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)  crossref  mathscinet  isi  scopus

99. 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  crossref  mathscinet  zmath  scopus (cited: 2)
100. 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  crossref  mathscinet  zmath  adsnasa  scopus (cited: 2)
101. 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  crossref  mathscinet  zmath  adsnasa  scopus (cited: 1)
102. 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)  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 11)
103. 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  mathnet

104. 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)  crossref  mathscinet  zmath  isi  scopus
105. 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  mathnet  mathscinet  adsnasa  adsnasa
106. 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  crossref  mathscinet  zmath  scopus (cited: 3)
107. 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  mathnet  mathscinet  adsnasa

108. 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  mathscinet

109. 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  crossref  mathscinet  zmath  scopus (cited: 21)

110. A. G. Kulikovskii, G. Ya. Galin, “Stability of one-dimensional gas flows in expanding regions”, Fluid Dynam., 16:2 (1981), 246–252  crossref  mathscinet  zmath  adsnasa  scopus (cited: 2)

111. 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)  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 10)

112. A. G. Kulikovskii, “Properties of shock adiabats in the neighborhood of Jouguet points”, Fluid Dynam., 14:2 (1979), 317–320  crossref  mathscinet  adsnasa  scopus (cited: 4)

113. 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  mathscinet  adsnasa

114. A. A. Barmin, A. G. Kulikovskiy, “Discontinuous solutions in mechanics of continua”, Fluid Mech.—Soviet Res., 8:6 (1979), 75–95 (1980)  mathscinet  zmath  scopus

115. 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  crossref  zmath  scopus

116. 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  crossref  mathscinet  adsnasa  scopus
117. 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  crossref  mathscinet  zmath  scopus (cited: 3)

118. A. G. Kulikovskii, F. A. Slobodkina, “Choice of a self-similar solution in boundary-layer theory”, Fluid Dynam., 9:4 (1974), 536–539  crossref  adsnasa  scopus (cited: 1)

119. 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  crossref  adsnasa  scopus (cited: 11)
120. 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  crossref  mathscinet  zmath  scopus (cited: 12)

121. A. A. Barmin, A. G. Kulikovskii, “Fronty ionizatsii i rekombinatsii v elektromagnitnom pole”, Itogi nauki. Gidrodinamika, 5, VINITI, M., 1971, 5–31
122. 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  mathscinet
123. 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  mathnet  adsnasa  adsnasa

124. A. G. Kulikovskii, F. A. Slobodkina, “Equilibrium of arbitrary steady flows at the transonic points”, J. Appl. Math. Mech., 31 (1968), 623–630  crossref  mathscinet  scopus (cited: 10)
125. A. G. Kulikovskii, “O poverkhnostyakh razryva, razdelyayuschikh idealnye sredy s razlichnymi svoistvami. Volny rekombinatsii”, PMM, 32:6 (1968), 1125–1131  zmath
126. A. A. Barmin, A. G. Kulikovskii, “Ob udarnykh volnakh, ionizuyuschikh gaz, nakhodyaschikhsya v elektromagnitnom pole”, Dokl. AN SSSR, 178:1 (1968), 55–58  mathnet (cited: 5)

127. S. V. Iordanskii, A. G. Kulikovskii, “A quasilinear approximation and the correlation functions for a plasma”, Soviet Physics JETP, 19 (1964), 499–506  mathscinet
128. S. V. Iordanskii, A. G. Kulikovskii, “A general stability condition for higher correlation functions in a plasma”, Soviet Phys. Dokl., 9 (1964), 347–349  mathnet  mathscinet  mathscinet  adsnasa

129. S. V. Iordanskii, A. G. Kulikovskii, “Stability of the higher correlation functions in a plasma”, Dokl. AN SSSR, 152 (1963), 849–852  mathnet  mathscinet  mathscinet

130. A. G. Kulikovskii, “On the structure of shock waves in magnetohydrodynamics with arbitrary dissipation law”, J. Appl. Math. Mech., 26 (1962), 392–400  crossref  mathscinet  scopus (cited: 3)
131. A. G. Kulikovskii, “The structure of shock waves”, J. Appl. Math. Mech., 26 (1962), 950–964  crossref  mathscinet  zmath  scopus (cited: 7)

132. A. G. Kulikovskii, G. A. Liubimov, “On the structure of an inclined magnetohydrodynamic shock wave”, J. Appl. Math. Mech., 25 (1961), 171–179  crossref  mathscinet  scopus (cited: 10)
133. A. G. Kulikovskii, “On the structure of slow magnetohydrodynamic shock waves in the barotropic case”, Sov. Phys. Dokl., 6 (1961), 302–304  mathnet  mathscinet  mathscinet  zmath  adsnasa

134. A. G. Kulikovskii, G. A. Lyubimov, “On gas-ionizing magnetohydrodynamic shock waves”, Rev. Mod. Phys., 32 (1960), 977–979  crossref  mathscinet  adsnasa  elib  scopus (cited: 4)

135. 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  crossref  mathscinet  zmath  scopus

136. 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  mathscinet  zmath  adsnasa
137. A. G. Kulikovskii, G. A. Lyubimov, “Gas-ionizing magnetohydrodynamic shock waves”, Sov. Phys. Dokl., 4 (1960), 1185–1188  mathscinet  adsnasa

138. A. G. Kulikovskii, “On media in which unidimensional motions with homogeneous deformations are possible”, Dokl. AN SSSR, 120 (1958), 485–486  mathnet  mathscinet  mathscinet

139. A. G. Kulikovskij, “On motions with homogenous deformation in magneto-hydrodynamics”, Sov. Phys. Dokl., 3 (1959), 507–509  mathnet  mathscinet  mathscinet  zmath  adsnasa

140. A. G. Kulikovskii, “O volnakh Rimana v magnitnoi gidrodinamike”, Dokl. AN SSSR, 121 (1958), 987–990  mathnet  mathscinet  mathscinet  zmath

141. A. G. Kulikovskii, “Ob obtekanii namagnichennykh tel provodyaschei zhidkostyu”, Dokl. AN SSSR, 117 (1957), 199–202  mathnet (cited: 1)  mathscinet  mathscinet  zmath
142. A. G. Kulikovskii, “On the pulsation of plasma in a cylinder”, Dokl. Akad. Nauk SSSR, 114:5 (1957), 984–987  mathnet

143. A. G. Kulikovskii, “O vyrozhdenii odnorodnoi izotropnoi magnitogidrodinamicheskoi turbulentnosti v neszhimaemoi zhidkosti”, PMM, 19:5 (1955), 551–556  mathscinet  zmath

Presentations in Math-Net.Ru
1. О структурах разрывов в решениях гиперболических систем уравнений. Волны в стержнях. Особые разрывы
A. G. Kulikovskii, A. P. Chugainova
Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2021
November 24, 2021 12:20   
2. Разрывы в решениях уравнений МСС и их структура. Нелинейные волны в упругих стержнях.
A. G. Kulikovskii, A. P. Chugainova
Seminar of the Department of Mechanics
June 7, 2021 16:45   
3. Opening Speech
A. G. Kulikovskii
School for Young Mechanicians and Mathematicians “Mathematical Methods of Mechanics”
November 10, 2020 10:45
4. 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   
5. Об устойчивости структуры нейтрально устойчивой ударной волны в газе
A. G. Kulikovskii
Seminar of the Department of Mechanics
January 13, 2020 12:00
6. Особые разрывы в нелинейно-упругих анизотропных цилиндрах
A. P. Chugainova, A. G. Kulikovskii
Seminar of the Department of Mechanics
February 25, 2019 12:00
7. Развитие линейных возмущений поверхности тангенциального разрыва, разделяющего сталкивающиеся потоки идеальных несжимаемых жидкостей
A. G. Kulikovskii
Seminar of the Department of Mechanics
October 8, 2018 12:00
8. 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
9. Разрывные решения обобщенного уравнения Хопфа
A. G. Kulikovskii, A. P. Chugainova
Seminar of the Department of Mechanics
October 23, 2017 12:00
10. О применении комплексных уравнений Гамильтона для изучения развития возмущений на стационарном слабонеоднородном фоне
A. G. Kulikovskii
Seminar of the Department of Mechanics
January 18, 2016 12:00
11. Shock waves in elastoplastic media with a structure defined by the process of stress relaxation
A. P. Chugainova, A. G. Kulikovskii
International Conference on Mathematical Control Theory and Mechanics
July 6, 2015 10:40
12. Асимптотические подходы к изучению неустойчивости и эволюции возмущений в пространственно протяженных областях
A. G. Kulikovskii
International conference "Contemporary Problems of Mathematics, Mechanics, and Mathematical Physics" dedicated to the 150th anniversary of V. A. Steklov
May 14, 2013 11:00   
13. Разрывы в решениях уравнений механики сплошной среды. Ударные адиабаты
A. G. Kulikovskii
International conference "Contemporary Problems of Mechanics" dedicated to the 80th anniversary of academician A. G. Kulikovskii
March 18, 2013 11:50   
14. Дополнительные соотношения на разрывах в решениях гиперболических уравнений механики сплошной среды, фронты ионизации в магнитном поле
A. G. Kulikovskii
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
March 9, 2006
15. Influence of small-scale dispersion and dissipative processes on the formation of large-scale phenomena
A. G. Kulikovskii
Steklov Mathematical Institute Seminar
March 17, 2005 16:00   
16. On the nonuniqueness of solutions of the equations of the non-linear theory of elasticity
A. G. Kulikovskii
Steklov Mathematical Institute Seminar
December 13, 2001

Books in Math-Net.Ru
  1. 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.
  2. 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.
  3. 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.
  4. 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.

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