Stationary solutions for some shadow system of the Keller-Segel model with logistic growth

Tohru Tsujikawa, Kousuke Kuto, Yasuhito Miyamoto, Hirofumi Izuhara

研究成果: Article査読

3 被引用数 (Scopus)

抄録

From a viewpoint of the pattern formation, the Keller-Segel sys- tem with the growth term is studied. This model exhibited various static and dynamic patterns caused by the combination of three effects, chemotaxis, dif- fusion and growth. In a special case when chemotaxis effect is very strong, some numerical experiment in [1],[22] showed static and chaotic patterns. In this paper we consider the logistic source for the growth and a shadow system in the limiting case that a diffusion coefficient and chemotactic intensity grow to infinity. We obtain the global structure of stationary solutions of the shadow system in the one-dimensional case. Our proof is based on the bifurcation, sin- gular perturbation and a level set analysis. Moreover, we show some numerical results on the global bifurcation branch of solutions by using AUTO package.

本文言語English
ページ(範囲)1023-1034
ページ数12
ジャーナルDiscrete and Continuous Dynamical Systems - Series S
8
5
DOI
出版ステータスPublished - 2015 10 1
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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