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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 51

On the 85th Birthday Anniversary of the RAS Corresponding Member, Professor A. A. Tolstonogov

Author(s)
I. V. Bychkov1, V. A. Dykhta1, A. L. Kazakov1, N. I. Pogodaev1, V. A. Shelekhov1

1Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russian Federation

Abstract
The paper is dedicated to the scientific and scientific-pedagogical activities of the professor, Corresponding Member of the Russian Academy of Sciences A. A. Tolstonogov, who turns 85 in March 2025.
About the Authors

Igor V. Bychkov, Dr. Sci. (Tech.), Prof., Acad. of the RAS, Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, bychkov@icc.ru

Vladimir A. Dykhta, Dr. Sci. (Phys.-Math.), Prof., Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, dykhta@icc.ru

Alexander L. Kazakov, Dr. Sci. (Phys.-Math.), Prof., Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, kazakov@icc.ru

Nikolay I. Pogodaev, Cand. Sci. (Phys.–Math.), Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, nickpogo@gmail.com

Vladimir A. Shelekhov, Cand. Sci. (Tech.), Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, vash@icc.ru,

For citation

Bychkov I. V., Dykhta V. A.,Kazakov A. L.,Pogodaev N. I., Shelekhov V. A. On the 85th Birthday Anniversary of the RAS Corresponding Member, Professor A. A. Tolstonogov. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 51, pp. 167–178. (in Russian)

https://doi.org/10.26516/1997-7670.2025.51.167

Keywords
relaxation, subdifferential, sweeping process, nonconvex constraints
UDC
012
MSC
01A70
DOI
https://doi.org/10.26516/1997-7670.2025.51.167
References
  1. Tolstonogov A.A. Differencial’nye vklyucheniya v banahovom prostranstve [Differential inclusions in a Banach space]. Novosibirsk, Nauka Publ., 1986, 296 p. (in Russian)
  2. De Blasi F.S., Pianigiani G., Tolstonogov A.A. A Bogolyubov-type theorem with a nonconvex constraint in Banach spaces. SIAM J. Contr. Opt., 2005, vol. 43, no. 2, pp. 466–476. https://doi.org/10.1137/S0363012903423156
  3. Krejci P., Timoshin S.A., Tolstonogov A.A. Relaxation and optimisation of a phasefield control system with hysteresis. Int. J. Contr., 2018, vol. 91, no. 1, pp. 85–100. https://doi.org/10.1080/00207179.2016.1268270
  4. Pogodaev N.I., Tolstonogov A.A. The variational stability of an optimal control problem for Volterra-type equations. Sib. Math. J., 2014, vol. 55, no. 4, pp. 667–686. https://doi.org/10.1134/S0037446614040090
  5. Tolstonogov A.A. Comparison theorems for evolution inclusions with maximal monotone operators. L2-theory. Sb. Math., 2023, vol. 214, no. 6, pp. 853–877. https://doi.org/10.4213/sm9736e
  6. Tolstonogov A. Differential inclusions in a Banach space. Kluwer Academic Publishers, Dordrecht, Boston, London, 2000, 302 p. https://doi.org/10.1007/978-94-015-9490-5
  7. Tolstonogov A.A. Maximal Monotonicity of a Nemytskii Operator. Funct. Anal. Appl., 2021, vol. 55, no. 3, pp. 217–225. https://doi.org/10.4213/faa3892
  8. Tolstonogov A.A. Properties of Solutions of a Control System with Hysteresis. J. Math. Sci. (USA), 2014, vol. 196, no. 3, pp. 405–433. https://doi.org/10.1007/s10958-014-1665-x
  9. Tolstonogov A.A. Variational stability of optimal control problems involving subdifferential operators. Sb. Math., 2011, vol. 202, no. 4, pp. 583–619. https://doi.org/10.1070/SM2011v202n04ABEH004157
  10. Tolstonogov A.A., Tolstonogov D.A. Lp-continuous extreme selectors of multifunctions with decomposable values: Existence theorems. Set-Valued Anal., 1996, vol. 4, no. 2, pp. 1730–203. https://doi.org/10.1007/BF00425964
  11. Tolstonogov A.A., Tolstonogov D.A. Lp-continuous extreme selectors of multifunctions with decomposable values: Relaxation theorems. Set-Valued Anal., 1996, vol. 4, no. 3, pp. 237–269. https://doi.org/10.1007/BF00419367

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