Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics
- Gonzalo Galiano Casas
- M.L. Garzón
- Ansgar Jüngel
ISSN: 1578-7303
Year of publication: 2001
Volume: 95
Issue: 2
Pages: 281-296
Type: Article
More publications in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM )
Abstract
A nonlinear population model with cross-diffusion terms for two competing species is studied analytically and numerically. Due to the cross diffusion terms, the problem is strongly nonlinear and so, no maximum principle generally applies. We show first the existence of weak solutions to the parabolic system in any space dimension. Then the one-dimensional stationary problem is investigated analytically and the notion of segregation is discussed. Finally, we present numerical results for the one-dimensional stationary problem underlining the effects of segregation of the species.