Published Paper

Inserted: 4 aug 2025

Journal: Partial Differential Equations and Applications
Volume: 6
Number: 19
Year: 2025
Doi: https://doi.org/10.1007/s42985-025-00322-5

Abstract:

We investigate an infinite dimensional partial differential equation of Isaacs’ type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transportcontinuity equation, where the control is given by the velocity vector field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.

Keywords: Viscosity solutions, differential games, Mass transportation, zero-sum games, infinite-dimensional isaacs equations