Bardi, Martino; Soravia, Pierpaolo 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 Cited in 4 Documents MSC: 91A24 Positional games (pursuit and evasion, etc.) 91A23 Differential games (aspects of game theory) 91A99 Game theory 91A05 2-person games Keywords:viscosity solution; induced boundary value problem; minimum time problem Citations:Zbl 0663.00020; Zbl 0599.35024 × Cite Format Result Cite Review PDF