Multitime hybrid differential games with curvilinear integral functional

Abstract

Multitime differential games are related to the modeling and analysis of cooperation or conflict in the context of a multitime dynamical systems. Their theory involves either a curvilinear integral functional or a multiple integral functional and an $m$-flow as constraint. The aim of this paper is to give original results regarding multitime hybrid differential games with curvilinear integral functional constrained by an $m$-flow: fundamental properties of multitime upper and lower values, viscosity solutions of multitime (HJIU) PDEs, representation formula of viscosity solutions for multitime (HJ) PDEs, and max-min representations.