On Differential Games for Infinite-Dimensional Systems with Nonlinear, Unbounded Operators

We consider a two-player, zero-sum differential game governed by an abstract nonlinear differential equation of accretive type in an infinite-dimensional space. We prove that the value function of the game is the unique viscosity solution of the corresponding Hamilton]Jacobi]Isaacs equation in the sense of M. G. Crandall and P. L. Lions ‘‘Evolution Equations, Control Theory and Biomathematics,’’ Lecture Notes in Pure and Appl. Math., Vol. 155, Dekker, New York, 1994.. We also discuss some properties of this notion of solution.