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A PDE framework for games of pursuit-evasion type. (English) Zbl 0679.90109
Differential games and applications, Proc. 3rd Int. Symp., Sophia- Antipolis/Fr. 1988, Lect. Notes Control Inf. Sci. 119, 62-71 (1989).
[For the entire collection see Zbl 0663.00020.]
The paper considers a two-player differential game of the pursuit-evasion type. The main result is that the capture time is the unique solution, in the viscosity sense [see e.g., M. G. Crandall and P.-L. Lions, Trans. Am. Math. Soc. 277, 1-42 (1983; Zbl 0599.35024)] of the induced boundary value problem. An analogous result for the minimum time problem of optimal control theory was proved by M. Bardi [SIAM J. Control Optimization 27, No.4, 776-785 (1989)].
Reviewer: S.Jørgensen

91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)
91A99 Game theory
91A05 2-person games