Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 50, pp. 1-18.

Title: A minmax  problem for parabolic systems with  competitive interactions

Author: Sanjay Chawla (Univ. of Minnesota, Minneapolis, USA)

Abstract: 
 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.

Submitted June 16, 1999. Published December 13, 1999.
Math Subject Classifications: 49K35, 49K20, 49K22, 35K57, 45K05.
Key Words: optimal control; game theory; saddle point.