A zero-sum differential game for two opponent masses
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 transport/continuity 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.
Authors
- Luciano Marzufero (ORCID: https://orcid.org/0000-0003-4983-8712)
- Fabio Bagagiolo
- Rossana Capuani (ORCID: https://orcid.org/0000-0002-7352-6041)
Institutions
- University of Arizona (US)
- Free University of Bozen-Bolzano (IT)
- University of Trento (IT)
Publication Details
- Journal
- Partial Differential Equations and Applications
- Published
- 2025-04-16
- DOI
- https://doi.org/10.1007/s42985-025-00322-5
- Primary Topic
- Guidance and Control Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Università degli Studi di Trento
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni