Jeux différentiels et approximation numérique de fonctions valeur. I: Étude théorique. (Differential games and numerical approximation of value functions. I: Theoretical analysis). (French) Zbl 0734.90131

An antagonistic pursuit-evasion game on the plane is studied (as a model, the lion-antilope game is presented). It is a simple pursuit game.
The dynamic programming approach is used for the study of the value function for both players in the game under consideration. It is proved that the capture time is finite and satisfies some estimation conditions. The value functions for both players are bounded, Lipschitzian and are unique viscosity solutions of the corresponding Isaacs equations.
[For part II see the author, ibid. 25, No.5, 535-560 (1991; Zbl 0734.90132).]


91A24 Positional games (pursuit and evasion, etc.)
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
91A23 Differential games (aspects of game theory)


Zbl 0734.90132
Full Text: DOI EuDML


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