## Hiroshima Mathematical Journal

### Reaction-diffusion system approximation to the cross-diffusion competition system

#### Abstract

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 information

Source
Hiroshima Math. J., Volume 38, Number 2 (2008), 315-347.

Dates
First available in Project Euclid: 5 September 2008

https://projecteuclid.org/euclid.hmj/1220619462

Digital Object Identifier
doi:10.32917/hmj/1220619462

Mathematical Reviews number (MathSciNet)
MR2437576

Zentralblatt MATH identifier
1162.35387

#### Citation

Izuhara, Hirofumi; Mimura, Masayasu. Reaction-diffusion system approximation to the cross-diffusion competition system. Hiroshima Math. J. 38 (2008), no. 2, 315--347. doi:10.32917/hmj/1220619462. https://projecteuclid.org/euclid.hmj/1220619462