Geodesic
A minmax problem for parabolic systems with competitive interactions
Electronic journal of differential equations, Tome 1999 (1999)
Zbl   EuDML
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 
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/
@article{EJDE_1999__1999__a9,
     author = {Chawla,  Sanjay},
     title = {A minmax problem for parabolic systems with competitive interactions},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0935.49016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a9/}
}
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