Skip to main content
SpringerLink
Log in

In Memory of Nikolay Dmitrievich Kopachevsky, a Mathematician and a Human

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

This paper is dedicated to the scientific and pedagogical activities of Nikolay Dmitrievich Kopachevsky (1940–2020) — a well-known mathematician, head of the Department of Mathematical Analysis of the V. I. Vernadsky Crimean Federal University, organizer and head of the Crimean Autumn Mathematical School-Symposium (KROMSH).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. V. Andronov and N. D. Kopachevsky, “Self-adjoint operator pencils generated by problems on the oscillations of an ideal rotating fluid,” UkrNIINTI, Kiev, 12.0.86, No. 1667-YK-86 (1986).

  2. A. V. Andronov and N. D. Kopachevsky, “Small oscillations of an ideal stratified fluid in a container with a elastic bottom,” In: Problems of Hydromechanics and Heat and Mass Transfer with Free Boundaries, NGU, Novosibirsk, pp. 16–25 (1987).

  3. O. A. Andronova and N. D. Kopachevsky, “On linear problems with surface energy dissipation,” Sovrem. Mat. Fundam. Napravl., 29, 11–28 (2008).

    Google Scholar 

  4. T. Ya. Azizov, V. Hardt, N. D. Kopachevsky, and R. Mennicken, “On the problem of small motions and normal oscillations of a viscous fluid in a partially filled container,” Math. Nachr., 248-249, 3–39 (2003).

    Article  MathSciNet  Google Scholar 

  5. T. Ya. Azizov and N. D. Kopachevsky, Introduction to the Theory of Pontryagin Spaces: Special Course of Lectures [in Russian], Forma, Simferopol’ (2008).

  6. T. Ya. Azizov and N. D. Kopachevsky, Introduction to the Theory of Kreyn Spaces: Special Course of Lectures [in Russian], Forma, Simferopol’ (2010).

  7. T. Ya. Azizov and N. D. Kopachevsky, Applications of Indefinite Metric [in Russian], DIAYPI, Simferopol’ (2014).

  8. T. Ya. Azizov, N. D. Kopachevsky, and L. D. Orlova, “Evolution and spectral problems generated by the problem of small motions of a viscoelastic fluid,” Tr. SPb. Mat. Ob-va, 6, 5–33 (1998).

    Google Scholar 

  9. T. Ya. Azizov, N. D. Kopachevsky, and L. I. Suhocheva, “On eigenvalues of self-adjoint pencils with a parameter,” In: Proc OT16 Conference, Theta Foundation, Bucharest, pp. 37–50 (1997).

  10. V. G. Babsky, N. D. Kopachevsky, A. D. Myshkis, L. A. Slobozhanin, and A. D. Tyuptsov, Zero Gravity Hydromechanics [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  11. V. G. Babskii, N. D. Kopachevskii, A. D. Myshkis, L. A. Slobozhanin, and A. D. Tyuptsov, “On some unsolved problems of zero-gravity hydromechanics,” Nonlinear Anal., 4, No. 3, 607–621 (1980).

    Article  MathSciNet  Google Scholar 

  12. V. G. Babsky, M. Yu. Zhukov, N. D. Kopachevsky, A. D. Myshkis, L. A. Slobozhanin, and A. D. Tyuptsov, Methods for Solving Problems of Hydromechanics for Zero Gravity Conditions [in Russian], Naukova dumka, Kiev (1992).

  13. E. I. Batyr, O. A. Dudik, and N. D. Kopachevsky, “Small oscillations of bodies with cavities filled with an incompressible viscous fluid,” Izv. Vuzov. Severo-Kavkaz. Reg. Estestv. Nauki, S, 15–29 (2009).

  14. E. I. Batyr and N. D. Kopachevsky, “Small motions and normal oscillations in systems of connected gyrostats,” Sovrem. Mat. Fundam. Napravl., 49, 5–88 (2013).

    Google Scholar 

  15. E. L. Gaziev and N. D. Kopachevsky, “Small motions and eigenoscillations of a “fluid-barotropic gas” hydrosystem,” J. Math. Sci. (N.Y.), 192, No. 4, 389–416 (2013).

  16. E. L. Gaziev, N. D. Kopachevsky, and Z. Z. Sitshaeva, “On the inversion of the operator of potential energy in the problem of eigen oscillations of the system “capillary fluid — gas,” Dinam. Sist., 4, No. 1-2, 9–18 (2014).

    Google Scholar 

  17. I. Gohberg and S. Goldberg, Basic Operator Theory, Birkh¨auser, Boston–Basel–Berlin (1981).

  18. V. A. Grinshteyn, “Basis property of apart of the system of eigenvectors of a holomorphic operator function,” Mat. Zametki, 50, No. 1, 142–144 (1991).

    MathSciNet  Google Scholar 

  19. N. D. Kopachevsky, “On free oscillations of a fluid rotating in a cylindrical vessel under zero gravity,” Mekh. Zhidkosti i Gaza, No. 4, 3–9 (1972).

    Google Scholar 

  20. N. D. Kopachevsky, “Hydrodynamics in weak gravitational fields. On plane oscillations of an ideal fluid in a rectangular channel,” Mekh. Zhidkosti i Gaza, No. 5, 3–13 (1972).

  21. N. D. Kopachevsky, “On oscillations of immiscible fluids,” Zhurn. Vych. Mat. i Mat. Fiz., 13, No. 5, 1249–1263 (1973).

    MathSciNet  Google Scholar 

  22. N. D. Kopachevsky, “On oscillations of a capillary viscous rotating fluid,” Dokl. AN SSSR, 219, No. 5, 1065–1068 (1974).

    MathSciNet  Google Scholar 

  23. N. D. Kopachevsky, “Cauchy problem for small motions of an ideal capillary rotating fluid,” Dokl. AN SSSR, 219, No. 6, 1310–1313 (1974).

    MathSciNet  Google Scholar 

  24. N. D. Kopachevsky, “Application of Sobolev’s method to the problem of oscillations of an ideal capillary rotating fluid,” Zhurn. Vych. Mat. i Mat. Fiz., 16, No. 2, 426–439 (1976).

    Google Scholar 

  25. N. D. Kopachevsky, “Normal oscillations of a system of heavy viscous rotating fluids,” Dokl. AN USSR. Ser. A, No. 7, 586–590 (1978).

  26. N. D. Kopachevsky, “On the existence of surface waves in the problem of normal vibrations of an ideal fluid rotating in a partially filled vessel,” Funkts. Analiz i Ego Prilozh., 12, No. 2, 84–85 (1978).

    Google Scholar 

  27. N. D. Kopachevsky, “Basis properties of a system of eigenvectors and associated vectors of the self-adjoint operator pencil I − λA − λ−1B,” Funkts. Analiz i Ego Prilozh., 15, No. 2, 77–78 (1981).

    Google Scholar 

  28. N. D. Kopachevsky, “Inversion of the Lagrange theorem on the stability of small oscillations of a capillary viscous fluid,” Dokl. AN SSSR, 314, No. 1, 71–73 (1990).

    Google Scholar 

  29. N. D. Kopachevsky, “On the abstract Green formula for a triple of Hilbert spaces and its applications to the Stokes problem,” Tavr. Vestn. Inform. i Mat., No. 2, 52–80 (2004).

  30. N. D. Kopachevsky, “Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels,” Sovrem. Mat. Fundam. Napravl., 29, 71–102 (2008).

    Google Scholar 

  31. N. D. Kopachevsky, Spectral Theory of Operator Pencils: Special Course of Lectures [in Russian], Forma, Simferopol’ (2009).

  32. N. D. Kopachevsky, “My dear teacher A. D. Myshkis (on the occasion of his 90th birthday),” Zhurn. Mat. Fiz. Anal. i Geom., 6, No. 2, 1–17 (2010).

    Google Scholar 

  33. N. D. Kopachevsky, “Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms,” Sovrem. Mat. Fundam. Napravl., 57, 71–107 (2015).

    Google Scholar 

  34. N. D. Kopachevsky, Abstract Green’s Formula and Some of Its Applications [in Russian], Forma, Simferopol’ (2016).

  35. N. D. Kopachevsky and S. G. Krein, Operator Approach to Linear Problems of Hydrodynamics. Vol. 1: Self-Adjoint Problems for an Ideal Fluid, Birkh¨auser, Basel–Boston–Berlin (2001).

  36. N. D. Kopachevsky and S. G. Krein, Operator Approach to Linear Problems of Hydrodynamics. Vol. 2: Non-Self-Adjoint Problems for Viscous Fluids, Birkh¨auser, Basel–Boston–Berlin (2003).

  37. N. D. Kopachevsky and S. G. Kreyn, “Abstract Green formula for a triple of Hilbert spaces, abstract boundary-value and spectral problems,” Ukr. Mat. Vestn., 1, No. 1, 69–97 (2004).

    MathSciNet  Google Scholar 

  38. N. D. Kopachevsky, S. G. Kreyn, and Ngo Zuy Kan, Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  39. N. D. Kopachevsky, R. Mennicken, Yu. S. Pashkova, and C. Tretter, “Complete second-order linear differential operator equations in Hilbert space and applications in hydrodynamics,” Trans. Am. Math. Soc., 356, No. 12, 4737–4766 (2004).

    Article  MathSciNet  Google Scholar 

  40. N. D. Kopachevsky and A. D. Myshkis, “Hydrodynamics in weak force fields. On small oscillations of a viscous fluid in a potential field of mass forces,” Zhurn. Vych. Mat. i Mat. Fiz., 6, No. 6, 1054–1063 (1966).

    Google Scholar 

  41. N. D. Kopachevsky and A. D. Myshkis, “On free oscillations of a liquid self-gravitating ball with allowance for viscous and capillary forces,” Zhurn. Vych. Mat. i Mat. Fiz., 8, No. 6, 1291–1305 (1968).

    Google Scholar 

  42. N. D. Kopachevsky and Ngo Zuy Kan, “On one problem in the theory of free convection,” Dokl. AN SSSR, 251, No. 6, 1334–1337 (1980).

  43. N. D. Kopachevsky and Yu. S. Pashkova, “Small oscillations of a viscous fluid in a vessel bounded by an elastic membrane,” Russ. J. Math. Phys., 5, No. 4, 459–472 (1998).

    MathSciNet  Google Scholar 

  44. N. D. Kopachevsky and V. N. Pivovarchik, “On a sufficient condition for the instability of convective fluid motions in an open vessel,” Zhurn. Vych. Mat. i Mat. Fiz., 33, No. 1, 101–118 (1993).

    Google Scholar 

  45. N. D. Kopachevsky and K. A. Radomirskaya, “Abstract mixed boundary-value and spectral conjugation problems and their applications,” Sovrem. Mat. Fundam. Napravl., 61, 67–102 (2016).

    Google Scholar 

  46. N. D. Kopachevsky and N. K. Radyakin, “Free oscillations of two capillary fluids rotating in a cylindrical vessel,” Mekh. Zhidkosti i Gaza, No. 5, 97–104 (1976).

    Google Scholar 

  47. N. D. Kopachevsky and N. K. Radyakin, “On small oscillations of an ideal capillary fluid rotating in an axisymmetric vessel,” In: Issues of Comput. Math. and Tech., Naukova dumka, Kiev, pp. 3–25 (1976).

  48. N. D. Kopachevsky and N. K. Radyakin, “Two problems on normal oscillations of a system of low-viscosity capillary fluids,” In: Issues of Math. Phys. and Funct. Anal., Naukova dumka, Kiev, pp. 93–110 (1976).

  49. N. D. Kopachevsky and E. V. Semkina, “Linear Volterra integro-differential second-order equations unresolved with respect to the highest derivative,” Eurasian Math. J., 4, No. 4, 64–87 (2013).

    MathSciNet  Google Scholar 

  50. N. D. Kopachevsky and E. V. Semkina, “On small motions of hydraulic systems containing a viscoelastic fluid,” Itogi Nauki i Tekhn. Ser. Sovrem. Mat. i Ee Pril., 172, 48–90 (2019).

    Google Scholar 

  51. N. D. Kopachevsky and S. I. Smirnova, “Oscillations of a cylindrically inhomogeneous rotating fluid in a container of special form,” Spectral Evolution Probl., 3, 45–47 (1994).

    Google Scholar 

  52. N. D. Kopachevsky and S. I. Smirnova, “Proper oscillations of a cylindrically inhomogeneous fluid between coaxial cylinders,” Spectral Evolution Probl., 3, 44–45 (1994).

    Google Scholar 

  53. N. D. Kopachevsky and A. N. Temnov, “Oscillations of an ideal stratified fluid completely filling a vessel,” VINITI, Moskva, 02.03.82, No. 892-82 (1982).

  54. N. D. Kopachevsky and A. N. Temnov, “Oscillations of an ideal stratified fluid partially filling a vessel,” VINITI, Moskva, 28.12.82, No. 6398-82 (1982).

  55. N. D. Kopachevsky and A. N. Temnov, “Free oscillations of an ideal stratified fluid in a vessel,” Zhurn. Vych. Mat. i Mat. Fiz., 24, No. 1, 109–123 (1984).

    MathSciNet  Google Scholar 

  56. N. D. Kopachevsky and A. N. Temnov, “Oscillations of a stratified fluid in a free-form pool,” Zhurn. Vych. Mat. i Mat. Fiz., 26, No. 5, 734–755 (1986).

    Google Scholar 

  57. N. D. Kopachevsky, T. P. Temchenko, and M. Yu. Tsar’kov, “Oscillations of a system of layers of a stratified fluid in a cylindrical container,” UkrNIINTI, Simferopol’, 03.06.85, No. 1203 (1985).

  58. N. D. Kopachevsky and D. O. Tsvetkov, “Oscillations of stratified fluids,” Sovrem. Mat. Fundam. Napravl., 29, 103–130 (2008).

    Google Scholar 

  59. N. D. Kopachevsky and D. O. Tsvetkov, “Oscillations of stratificated fluids,” J. Math. Sci. (N.Y.), 164, No. 4, 574–602 (2010).

  60. N. D. Kopachevsky and D. O. Tsvetkov, “Small motions of an ideal stratified fluid in a basin covered with ice,” Sovrem. Mat. Fundam. Napravl., 64, No. 3, 573–590 (2018).

    Google Scholar 

  61. N. D. Kopachevsky and D. O. Tsvetkov, “Small motions of an ideal stratified fluid with a free surface completely covered with crushed ice,” Ufimsk. Mat. Zh., 18, No. 3, 44–59 (2018).

    Google Scholar 

  62. N. D. Kopachevsky and D. O. Tsvetkov, “The Cauchy problem generated by oscillations of a stratified fluid partially covered with ice,” Tavr. Vestn. Inform. i Mat., No. 1, 31–39 (2018).

  63. N. D. Kopachevsky and V. I. Voytitsky, “On small motions of a physical pendulum with a cavity filled with a system of three homogeneous immiscible viscous fluids,” Tavr. Vestn. Inform. i Mat., No. 3, 22–45 (2018).

  64. N. D. Kopachevsky and V. I. Voytitsky, “On oscillations of connected pendulums with cavities filled with homogeneous fluids,” Sovrem. Mat. Fundam. Napravl., 65, No. 3, 434–512 (2019).

    Google Scholar 

  65. N. D. Kopachevsky and V. I. Voytitsky, “On small vibrations of three connected pendulums with cavities filled with homogeneous ideal fluids,” Sib. Elektron. Mat. Izv., 17, 260–299 (2020).

    Article  Google Scholar 

  66. N. D. Kopachevsky, V. I. Voytitsky, and Z. Z. Sitshaeva, “On oscillations of two connected pendulums containing cavities partially filled with incompressible fluid,” Sovrem. Mat. Fundam. Napravl., 63, No. 4, 627–677 (2017).

    Google Scholar 

  67. N. D. Kopachevsky, V. I. Voytitsky, and Z. Z. Sitshaeva, “On two hydromechanical problems inspired by works of S. Krein,” In: Differential Equations, Mathematical Physics, and Applications. Selim Grigorievich Krein Centennial, AMS, Providence, pp. 219–238 (2019).

  68. N. D. Kopachevsky and A. R. Yakubova, “On some problems generated by a sesquilinear form,” Sovrem. Mat. Fundam. Napravl., 63, No. 2, 278–315 (2017).

    Google Scholar 

  69. A. S. Markus, Introduction to the Spectral Theory of Polynomial Operator Pencils [in Russian], Shtiintsa, Kishinev (1986).

  70. A. D. Myshkis, Soviet Mathematicians. My Memories [in Russian], Librokom, Moscow (2009).

  71. A. D. Myshkis, V. G. Babskii, N. D. Kopachevskii, L. A. Slobozhanin, and A. D. Tyuptsov, Low-Gravity Fluid Mechanics, Springer-Verlag, Berlin, etc. (1987).

    Book  Google Scholar 

  72. V. I. Voytitsky, N. D. Kopachevsky, and P. A. Starkov, “Multicomponent conjugation problems and auxiliary abstract boundary-value problems,” Sovrem. Mat. Fundam. Napravl., 34, 5–44 (2009).

    Google Scholar 

  73. B. M. Vronsky, N. D. Kopachevsky, and T. P. Temchenko, “Oscillations of partially dissipative hydraulic systems,” In: XII School on the Theory of Operators in Function Spaces, Tambov, pp. 40 (1987).

  74. B. M. Vronsky and N. D. Kopachevsky, “On one estimate of an operator function,” Uch. Zap. Tavr. Nats. Un-ta Im. V. I. Vernadskogo. Ser. Fiz.-Mat. Nauki, 23, No. 1, 51–54 (2010).

  75. D. A. Zakora and N. D. Kopachevsky, “On small motions and normal oscillations of the hydraulic system “viscous fluid + system of ideal fluids,” Mat. Fiz. Anal. Geom., 9, No. 3, 420–426 (2002).

    MathSciNet  Google Scholar 

  76. D. A. Zakora and N. D. Kopachevsky, “To the problem on small oscillations of a system of two viscoelastic fluids filling immovable vessel: model problem,” Sovrem. Mat. Fundam. Napravl., 66, No. 2, 182–208 (2020).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. I. Vernadsky Crimean Federal University, Simferopol, Russia

    V. I. Voytitsky, M. A. Muratov, Yu. S. Pashkova, P. A. Starkov & D. O. Tsvetkov

  2. Saint Petersburg State University, Saint Petersburg, Russia

    T. A. Suslina

Authors
  1. V. I. Voytitsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Muratov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. S. Pashkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. A. Starkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. T. A. Suslina
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. D. O. Tsvetkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Voytitsky.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Voytitsky, V.I., Muratov, M.A., Pashkova, Y. et al. In Memory of Nikolay Dmitrievich Kopachevsky, a Mathematician and a Human. J Math Sci 278, 1–11 (2024). https://doi.org/10.1007/s10958-024-06902-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-024-06902-x

Search

Navigation