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Mat. Sb. (N.S.), 1977, Volume 103(145), Number 3(7), Pages 430–444 (Mi msb2916)  

This article is cited in 6 scientific papers (total in 6 papers)

On the theory of differential games of escape

N. Yu. Satimov


Abstract: The paper consists of three sections. In § 1 a simplified proof is obtained of Pontryagin's escape theorem, differing from his in that in the so-called fine case no integral equation is solved. In § 2, at the expense of restricting the class of controls available to the pursuer, the theory is in a definite sense freed of the constant $\mu$ occurring in Pontryagin's escape theorem. In § 3 a sufficient escape condition is presented for quasilinear games, and examples are also considered.
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 32:3, 371–383

Bibliographic databases:

UDC: 517.9
MSC: 90D25
Received: 23.12.1976

Citation: N. Yu. Satimov, “On the theory of differential games of escape”, Mat. Sb. (N.S.), 103(145):3(7) (1977), 430–444; Math. USSR-Sb., 32:3 (1977), 371–383

Citation in format AMSBIB
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\by N.~Yu.~Satimov
\paper On the theory of differential games of escape
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 103(145)
\issue 3(7)
\pages 430--444
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=475941}
\zmath{https://zbmath.org/?q=an:0364.90137|0396.90117}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 3
\pages 371--383
\crossref{https://doi.org/10.1070/SM1977v032n03ABEH002392}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977GK37400007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mishchenko E. Satimov N., “An Encounter-Evasion Problem in the Critical Case”, Differ. Equ., 19:2 (1983), 160–167  mathscinet  zmath  isi
    2. Satimov N., “Generalizations of Pontryagin,l.S. Lemma Concerning Squares”, Differ. Equ., 20:9 (1984), 1118–1123  mathscinet  zmath  isi
    3. Satimov N., “Possibility of Encounter Avoidance in a Critical Case”, Differ. Equ., 20:12 (1984), 1451–1455  mathscinet  zmath  isi
    4. Konovalov A., “Nonlinear Differential Encounter-Evasion Games with Delay”, 23, no. 3, 1987, 418–425  mathscinet  zmath  isi
    5. J. Yong, “A sufficient condition for the evadability of differential evasion games”, J Optim Theory Appl, 57:3 (1988), 501  crossref  mathscinet  zmath  isi
    6. Jiongmin Yong, “On the evadable sets of differential evasion games”, Journal of Mathematical Analysis and Applications, 133:1 (1988), 249  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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