Russian Mathematical Surveys, 2024, Volume 79, Issue 5, Pages 919–921 DOI: https://doi.org/10.4213/rm10196e (Mi rm10196)

DOI: https://doi.org/10.4213/rm10196e

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On 30 May 2024 the member of Russian Academy of Sciences, chief researcher of the Department of Mechanics of the V. A. Steklov Mathematical Institute of Russian Academy of Sciences Andrei Gennad’evich Kulikovskii passed away. He was a prominent expert in mechanics, one of the brightest representatives of the Russian school in fluid mechanics, always excited by new fruitful research ideas and plans.

In 1955 Kulikovskii graduated from the Faculty of Mechanics and Mathematics at Moscow State University and enrolled for graduate studies at the same faculty, in the Department of Hydromechanics. Academician Leonid Ivanovich Sedov was his scientific advisor. His first research papers, and then also his Ph.D. thesis were devoted to magnetic hydrodynamics, which was a new area of continuum mechanics at that time. Investigations of problems in magnetic hydrodynamics laid the groundwork for the study of complicated models in continuum mechanics, which are described by nonlinear hyperbolic equations. Jointly with G. A. Lyubimov they published the monograph Magnetic hydrodynamics [1], which became a classic textbook. In conjunction with G. A. Lyubimov and A. A. Barmin, Kulikovskii investigated discontinuities in magnetic hydrodynamics, which are ionization and recombination fronts. Certain additional boundary conditions must be satisfied on this discontinuities, which follow from the assumption that a discontinuity structure exists. The number of this conditions depends on the rate of the discontinuity. Kulikovskii showed that not only for these discontinuities, but also in a quite general setting the number of the additional conditions on a discontinuity that follow from the assumption of the existence of a discontinuity structure, ensures that the discontinuity is evolutionary.

In 1958, upon finishing his postgraduate education, Kulikovskii was hired by the Department of Mechanics of the Steklov Mathematical Institute, where he worked for more than 65 years. Till the last day of his life he remained one of the most energetic researchers at the department.

Another area of Kulikovskii’s research was related to the stability and development of perturbations in extended domains. He showed that in the case of a homogeneous flow, instability can arise in twow forms, the boundary form produced by the interaction of the equations with the boundary data, and the global form produced by the amplification of the wave travelling towards another boundary and reflecting from it. For these results, in 1967 Kulikovskii was awarded the S. A. Chaplygin Prize. As a further development of the subject he wrote a cycle of papers on criteria for instability and evolution of perturbations against a slowly varying steady-state background.

The expertise gained in the solution of problems in magnetic hydrodynamics was used in the construction and investigation of other models in continuum mechanics that are described by systems of nonlinear hyperbolic equations. Together with E. I. Sveshnikova, Kulikovskii considered nonlinear waves in weakly anisotropic elastic media. They were the subject of the monograph Nonlinear waves in elastic media [2].

A large cycle of papers on nonlinear waves was written by Kulikovskii with A. P. Chugainova. They considered the lack of uniqueness of solutions of the Riemann problem and the role of non-classical discontinuities in these solutions.

For his results on nonlinear waves is continuous media Kulikovskii (as a member of the research team) was awarded the State Prize of the Russian Federation in 2003.

Till his last days Kulikovskii continued research in several directions at a time. here are his main results of recent years: with A. T. Il’ichev, A. V. Shargatov, and Chugainova he investigated the stability of the structure of a neutrally stable shock wave, which is also called a spontaneously radiating wave [3]; together with J. S. Zayko he found the asymptotic behaviour of a localized perturbation in the flow of a viscous fluid going down an incline [4]; together with Chugainova he studied non-classical discontinuities in solutions of a system of nonlinear hyperbolic equations describing longitudinal–torsional waves in media with dispersion and dissipation [5], [6].  

Kulikovskii always placed great emphasis on teaching. For many years he was a professor at the Department of Hydromechanics of Lomonosov Moscow State University, and many of his students obtained Ph.D. and D.Sc. degrees and developed into well-known scientists.

A remarkable person, prominent researcher and teacher has gone.

Bibliography
1.	A. G. Kulikovskii and G. A. Lyubimov, Margentic hydrodynamics, 2nd revised and augmented ed., Logos, Moscow, 2005, 328 pp. (Russian)
2.	A. Kulikovskii and E. Sveshnikova, Nonlinear waves in elastic media, CRC Press, Boca Raton, FL, 1995, x+237 pp.
3.	A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, and V. A. Shargatov, “On the structure stability of a neutrally stable shock wave in a gas and on spontaneous emission of perturbations”, JETP, 131:3 (2020), 481–495
4.	A. Kulikovskii and J. Zayko, “Asymptotic behavior of localized disturbance in a viscous fluid flow down an incline”, Phys. Fluids, 34:3 (2022), 034119, 12 pp.
5.	A. G. Kulikovskii and A. P. Chugainova, “Structures of non-classical discontinuities in solutions of hyperbolic systems of equations”, Russian Math. Surveys, 77:1 (2022), 47–79
6.	A. P. Chugainova and A. G. Kulikovskii, “Structures of longitudinal-torsional shock waves and special discontinuities in nonlinearly viscoelastic media with dispersion”, Contin. Mech. Thermodyn., 35:4 (2023), 1655–1669

Citation in format AMSBIB

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\paper Andrei Gennad'evich Kulikovskii (obituary)
\jour Russian Math. Surveys
\yr 2024
\vol 79
\issue 5
\pages 919--921
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