We study the stationary problem of a reaction-diffusion system with a small parameter $\varepsilon$, which approximates the cross-diffusion competition system proposed to study spatial segregation problem between two competing species. The convergence between two systems as $\varepsilon \downarrow 0$ is discussed from analytical and complementarily numerical point of views.
@article{1220619462,
author = {Izuhara, Hirofumi and Mimura, Masayasu},
title = {Reaction-diffusion system approximation to the cross-diffusion competition system},
journal = {Hiroshima Math. J.},
volume = {38},
number = {1},
year = {2008},
pages = { 315-347},
language = {en},
url = {http://dml.mathdoc.fr/item/1220619462}
}
Izuhara, Hirofumi; Mimura, Masayasu. Reaction-diffusion system approximation to the cross-diffusion competition system. Hiroshima Math. J., Tome 38 (2008) no. 1, pp. 315-347. http://gdmltest.u-ga.fr/item/1220619462/