Geodesic
A minmax problem for parabolic systems with competitive interactions
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 49K35, 49K20, 49K22, 35K57, 45K05
Keywords: optimal control, game theory, saddle point 
@article{EJDE_1999__1999__a9,
     author = {Chawla, Sanjay},
     title = {A minmax problem for parabolic systems with competitive interactions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a9/}
}
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Chawla, Sanjay. A minmax problem for parabolic systems with competitive interactions. Electronic Journal of Differential Equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a9/