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Pursuit-evasion problems and viscosity solutions of Isaacs equations. (English) Zbl 0786.35018

A general existence result for the Dirichlet problem for first-order Hamilton-Jacobi equations arising from differential games of pursuit and evasion, is obtained in the class of viscosity solutions. Several comparison results between the value functions of a differential game and the continuous viscosity sub- or supersolutions of the corresponding Isaacs equation are proven and used in the existence results. The approach used allows Lyapunov functions satisfying the usual condition in the weak sense of viscosity solutions.

MSC:

35B37 PDE in connection with control problems (MSC2000)
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
91A23 Differential games (aspects of game theory)
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