A RELATION BETWEEN CROSS-DIFFUSION AND REACTION-DIFFUSION

作者：Murakawa Hideki^*

来源：Discrete and Continuous Dynamical Systems - Series S, 2012, 5(1): 147-158.

DOI：10.3934/dcdss.2012.5.147

• Cross-diffusion system
• Reaction-diffusion system
• Approximation

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 by reaction-diffusion interaction.

• 出版日期2012-2