Differential game with switching controls on Hilbert space

Abstract

We study differential game problems in which the players can select different maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elliott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assuming condition analogous to the classical Isaacs condition, and thus the existence of value of the game follows. © Australian Mathematical Society, 1997.