On the Value Function of a Differential Game with Simple Dynamics and Piecewise Linear Data*

A differential game with simple motions is considered under assumptions that the Hamiltonian and the cost terminal function are piecewise linear and positively homogeneous. The structure of the value function of the differential game is investigated in the framework of the theory of minimax (or/and viscosity) solutions for Hamilton-Jacobi equations. Inequalities are provided to estimate the value function. Cases of explicit formulas for the value function are pointed out.