A relation between cross-diffusion and reaction-diffusion

Hideki Murakawa

研究成果: ジャーナルへの寄稿学術誌査読

13 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)147-158
ページ数12
ジャーナルDiscrete and Continuous Dynamical Systems - Series S
5
1
DOI
出版ステータス出版済み - 2月 2012

!!!All Science Journal Classification (ASJC) codes

  • 分析
  • 離散数学と組合せ数学
  • 応用数学

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