A relation between cross-diffusion and reaction-diffusion
Hideki Murakawa · Discrete and Continuous Dynamical Systems - S · 2011
Reaction-diffusion system approximations to a cross-diffusion system are investigated.Iida and Ninomiya~[Recent Advances on Elliptic and Parabolic Issues, 145--164 (2006)] proposed a semilinear reaction-diffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled cross-diffusion system provided that solutions of both the reaction-diffusion and the cross-diffusion systems are sufficiently smooth.In this paper, the results are extended to a more general cross-diffusion problem involving strongly coupled systems.It is shown that a solution of the problem can be approximated by that of a semilinear reaction-diffusion system without any assumptions on the solutions.This indicates that the mechanism of cross-diffusion might be captured byreaction-diffusion interaction.