Geodesic
A minmax problem for parabolic systems with competitive interactions
Electronic journal of differential equations, Tome 1999 (1999)
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__a58,
     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__a58/}
}
TY  - JOUR
AU  - Chawla,  Sanjay
TI  - A minmax problem for parabolic systems with competitive interactions
JO  - Electronic journal of differential equations
PY  - 1999
VL  - 1999
UR  - http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a58/
LA  - en
ID  - EJDE_1999__1999__a58
ER  - 
%0 Journal Article
%A Chawla,  Sanjay
%T A minmax problem for parabolic systems with competitive interactions
%J Electronic journal of differential equations
%D 1999
%V 1999
%U http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a58/
%G en
%F EJDE_1999__1999__a58
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__a58/