### 抄録

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 |

巻 | 16 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 1982 12 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### これを引用

*Journal of Mathematical Biology*,

*16*(1), 1-24. https://doi.org/10.1007/BF00275157

**Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics.** / Ishii, Hitoshi; Takagi, Izumi.

研究成果: Article

*Journal of Mathematical Biology*, 巻. 16, 番号 1, pp. 1-24. https://doi.org/10.1007/BF00275157

}

TY - JOUR

T1 - Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

AU - Ishii, Hitoshi

AU - Takagi, Izumi

PY - 1982/12

Y1 - 1982/12

N2 - 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.

AB - 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.

KW - Global stability

KW - Nonlinear diffusion equation

KW - Self-shading

UR - http://www.scopus.com/inward/record.url?scp=0020464810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020464810&partnerID=8YFLogxK

U2 - 10.1007/BF00275157

DO - 10.1007/BF00275157

M3 - Article

AN - SCOPUS:0020464810

VL - 16

SP - 1

EP - 24

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

ER -