Geodesic
Reaction-diffusion systems with 1-homogeneous non-linearity
Electronic journal of differential equations, Tome 2002 (2002)
We describe the dynamics of a system of two reaction-diffusion equations with 1-homogeneous non-linearity. We show that either an order-preserving property holds and can be used in order to determine the limiting behaviour in some (invariant) sets or the long time behaviour of all solutions can be described by looking at one scalar reaction-diffusion equation only.
Classification : 35K57
Keywords: reaction-diffusion equations, order-preserving, reduction to one equation 
@article{EJDE_2002__2002__a223,
     author = {B\"uger,  Matthias},
     title = {Reaction-diffusion systems with 1-homogeneous non-linearity},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1029.35115},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a223/}
}
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%A Büger,  Matthias
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%J Electronic journal of differential equations
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%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a223/
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%F EJDE_2002__2002__a223
Büger,  Matthias. Reaction-diffusion systems with 1-homogeneous non-linearity. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a223/