Multitime hybrid differential games with multiple integral functional

Abstract

The purpose of this paper to formulate and to prove theorems about multitime differential games based on a multiple integral functional and an m-flow as constraint. The most important idea is to use a generating vector field for value functions. The original results include: fundamental properties of multitime upper and lower values, viscosity solutions of multitime (dHJIU) PDEs, representation formula of viscosity solutions for a multitime (dHJ) PDE, and max–min representations. These problems are totally new in the related literature, excepting our papers announced in arXiv.