Small BV solutions of hyperbolic noncooperative differential games

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Abstract

The paper is concerned with an n-person differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the noncooperative differential game.

Original languageEnglish (US)
Pages (from-to)194-215
Number of pages22
JournalSIAM Journal on Control and Optimization
Volume43
Issue number1
DOIs
StatePublished - Mar 9 2005

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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