ASYMPTOTIC PROPERTIES OF MINIMAX SOLUTIONS OF ISAACS-BELLMAN EQUATIONS IN DIFFERENTIAL GAMES WITH FAST AND SLOW MOTIONS

Abstract Sufficient conditions under which the solutions of the Cauchy problem for singularly-perturbed Hamilton-Jacobi equations will converge to a limit are established. The results are used to investigate the asymptotic behaviour of the value function of a differential game involving fast and slow motions.