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Mat. Zametki, 2006, Volume 80, Issue 4, Pages 613–626 (Mi mz2854)  

This article is cited in 10 scientific papers (total in 10 papers)

Game problems on a fixed interval in controlled first-order evolution equations

N. Yu. Satimov, M. Tukhtasinov

National University of Uzbekistan named after M. Ulugbek

Abstract: This paper is devoted to the study of pursuit and evasion problems on a fixed finite closed interval in controlled equations of parabolic type. The control parameters appear on the right-hand side of the equations in additive form. We study all possible cases of control constraints. For certain cases, we single out pairs of sets of initial positions for which the completion of the pursuit from points of the first set is guaranteed and an evasion of the terminal set is ensured in the case of initial points from the second set.


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English version:
Mathematical Notes, 2006, 80:4, 578–589

Bibliographic databases:

UDC: 517.95
Received: 03.06.2005

Citation: N. Yu. Satimov, M. Tukhtasinov, “Game problems on a fixed interval in controlled first-order evolution equations”, Mat. Zametki, 80:4 (2006), 613–626; Math. Notes, 80:4 (2006), 578–589

Citation in format AMSBIB
\by N.~Yu.~Satimov, M.~Tukhtasinov
\paper Game problems on a fixed interval in controlled first-order evolution equations
\jour Mat. Zametki
\yr 2006
\vol 80
\issue 4
\pages 613--626
\jour Math. Notes
\yr 2006
\vol 80
\issue 4
\pages 578--589

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    This publication is cited in the following articles:
    1. Sh. Alimov, “On the null-controllability of the heat exchange process”, Eurasian Math. J., 2:3 (2011), 5–19  mathnet  mathscinet  zmath
    2. Ja'afaru A.B., Ibragimov G., “On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First-Order Differential Equations”, J. Appl. Math., 2012, 717124  crossref  mathscinet  zmath  isi  scopus
    3. A. S. Bannikov, “Nekotorye nestatsionarnye zadachi gruppovogo presledovaniya”, Izv. IMI UdGU, 2013, no. 1(41), 3–46  mathnet
    4. M. Sh. Mamatov, Kh. N. Alimov, “Solving a pursuit problem in high-order controlled distributed systems”, Siberian Adv. Math., 24:4 (2014), 229–239  mathnet  crossref  mathscinet
    5. Salimi M., Ibragimov G.I., Siegmund S., Sharifi S., “On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints”, Dyn. Games Appl., 6:3 (2016), 409–425  crossref  mathscinet  zmath  isi  elib  scopus
    6. Ibragimov G., Akhmedov A., Izzati P.N., Manaf A.N., “Pursuit Differential Game Described By Infinite First Order 2-Systems of Differential Equations”, Malays. J. Math. Sci., 11:2 (2017), 181–190  mathscinet  isi
    7. Waziri U., Ibragimov G., Alias I.A., Ibrahim Z.B., 3Rd International Conference on Mathematical Sciences and Statistics, Journal of Physics Conference Series, 1132, eds. Chen C., Lee L., Kilicman A., Ismail F., Midi H., Gafurjan I., Husain S., Ibrahim S., IOP Publishing Ltd, 2018  crossref  isi
    8. M. Sh. Mamatov, Kh. Kh. Sobirov, “K teorii differentsialnykh igr presledovaniya po pozitsii”, Materialy nauchnoi konferentsii «Problemy sovremennoi topologii i ee prilozheniya», 11–12 Maya 2017 g., Tashkent, Uzbekistan, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 144, VINITI RAN, M., 2018, 39–46  mathnet  mathscinet
    9. Ibragimov G., Alias I.A., Waziri U., Ja'afaru A.B., “Differential Game of Optimal Pursuit For An Infinite System of Differential Equations”, Bull. Malays. Math. Sci. Soc., 42:1 (2019), 391–403  crossref  mathscinet  zmath  isi  scopus
    10. Tukhtasinov M. Mustapokulov K. Ibragimov G., “Invariant Constant Multi-Valued Mapping For the Heat Conductivity Problem”, Malays. J. Math. Sci., 13:1 (2019), 61–74  mathscinet  isi
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