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<p>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.</p>

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A zero-sum differential game for two opponent masses

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月16日

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  • Fabio Bagagiolo,
  • Rossana Capuani,
  • Luciano Marzufero

摘要

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.