# Viscosity solutions of divergence type PDEs associated to multitime hybrid games

## TL;DR

This paper introduces a new framework for multitime hybrid games, defining value functions, formulating divergence type PDEs, and establishing viscosity solutions to analyze complex multi-agent systems with integral and flow constraints.

## Contribution

It develops the first formulation of divergence type PDEs and viscosity solutions specifically for multitime hybrid games with multiple players and integral-functional constraints.

## Key findings

- Defined multitime lower and upper value functions
- Constructed divergence type PDEs for the game
- Established viscosity solutions for these PDEs

## Abstract

Our original results are associated to a multitime hybrid game, with two equips of players, based on a multiple integral functional and an m- ow as constraint. The aim of this paper is three-fold: (i) to define the multitime lower or upper value function; (ii) to build Divergence type PDEs ; (iii) to give viscosity solutions of previous PDEs.