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.
CitationChawla, S. (1999). A minmax problem for parabolic systems with competitive interactions. Electronic Journal of Differential Equations, 1999(50), pp. 1-18.
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