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.
"Reaction-diffusion system approximation to the cross-diffusion competition system." Hiroshima Math. J. 38 (2) 315 - 347, July 2008. https://doi.org/10.32917/hmj/1220619462