Min-max differential game with partial differential equation

Abstract

In this paper, we are concerned with a min-max differential game with Cauchy initial value problem (CIVP) as the state trajectory for the differential game, we studied the analytical solution and the approximate solution by using Picard method (PM) of this problem. We obtained the equivalent integral equation to the CIVP. Also, we suggested a method for solving this problem. The existence, uniqueness of the solution and the uniform convergence are discussed for the two methods.

Keywords

• cauchy initial value problem
• min-max differential game
• uniform convergence
• existence
• uniqueness
• picard method