A relation between cross-diffusion and reaction-diffusion

Hideki Murakawa

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)147-158
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue number1
Publication statusPublished - Feb 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'A relation between cross-diffusion and reaction-diffusion'. Together they form a unique fingerprint.

Cite this