A minmax problem for parabolic systems with competitive interactions

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In this paper we model the evolution and interaction between two competing populations as a system of parabolic partial differential equations. The interaction between the two populations is quantified by the presence of non-local terms in the system of equations. We model the whole system as a two-person zero-sum game where the gains accrued by one population necessarily translate into the others loss. For a suitably chosen objective functional(pay-off) we establish and characterize the saddle point of the game. The controls(strategies) are kernels of the interaction terms.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalElectronic Journal of Differential Equations
Publication statusPublished - 13 Dec 1999



  • Game theory
  • Optimal control
  • Saddle point

ASJC Scopus subject areas

  • Analysis

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