Diffusion, cross-diffusion and competitive interaction

In the field of population dynamics, some models of competing species are described by reaction-diffusion systems. Among them, there is a system which is taken into account the population pressure created by the competitors. It is called a cross-diffusion and competition system in mathematical biology. This system, especially, the global structures of equilibrium solutions have been investigated in nonlinear PDE communities. From the biological motivation, we discuss that such a cross-diffusion system can be approximated by a kind normal diffusion system, taking some singular limit.

This is a joint work with H. Ninomiya (Ryukoku Univ.) and M. Iida(Iwate Univ.).