On game problems for second-order evolution equations.

*(English. Russian original)*Zbl 1207.49048
Russ. Math. 51, No. 1, 49-57 (2007); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 1, 54-62 (2007).

From the introduction: In this paper, we consider certain problems of the theory of differential games in systems with distributed parameters. The players influence on the system with the use of control parameters contained in the right-hand side of the equation. Controls of players are chosen in the form of functions on which various constraints are imposed, so-called geometric, integral, and mixed constraints.

In the first three games, the goal of the first player is to bring the system into an unperturbed state. In the fourth game, the goal of the first player is to bring the system and its velocity into an arbitrary \(\ell\)-neighborhood of zero. The second player in all the games has the opposite goal.We present conditions which are sufficient in order that the first player can reach the goal in a finite time. For the third game, we also consider the encounter-evasion problem.

In the first three games, the goal of the first player is to bring the system into an unperturbed state. In the fourth game, the goal of the first player is to bring the system and its velocity into an arbitrary \(\ell\)-neighborhood of zero. The second player in all the games has the opposite goal.We present conditions which are sufficient in order that the first player can reach the goal in a finite time. For the third game, we also consider the encounter-evasion problem.

##### MSC:

49N75 | Pursuit and evasion games |

91A23 | Differential games (aspects of game theory) |

35J25 | Boundary value problems for second-order elliptic equations |

35L05 | Wave equation |

35L15 | Initial value problems for second-order hyperbolic equations |

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\textit{N. Yu. Satimov} and \textit{M. Tukhtasinov}, Russ. Math. 51, No. 1, 49--57 (2007; Zbl 1207.49048); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 1, 54--62 (2007)

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##### References:

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