A relation between cross-diffusion and reaction-diffusion

Hideki Murakawa

    Research output: Contribution to journalArticlepeer-review

    14 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


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