Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

Hitoshi Ishii, Izumi Takagi

研究成果: Article

33 引用 (Scopus)

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We consider a nonlinear diffusion equation proposed by Shigesada and Okubo which describes phytoplankton growth dynamics with a selfs-hading effect. We show that the following alternative holds: Either (i) the trivial stationary solution which vanishes everywhere is a unique stationary solution and is globally stable, or (ii) the trivial solution is unstable and there exists a unique positive stationary solution which is globally stable. A criterion for the existence of positive stationary solutions is stated in terms of three parameters included in the equation.

元の言語English
ページ(範囲)1-24
ページ数24
ジャーナルJournal of Mathematical Biology
16
発行部数1
DOI
出版物ステータスPublished - 1982 12
外部発表Yes

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

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