### Abstract

For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.

Original language | English (US) |
---|---|

Pages (from-to) | 534-543 |

Number of pages | 10 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 47 |

Issue number | 3 |

State | Published - Jun 1987 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER : DEPENDENCE ON CYLINDER WIDTH.** / Bell, Jonathan; Cosner, George.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 47, no. 3, pp. 534-543.

}

TY - JOUR

T1 - WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER

T2 - DEPENDENCE ON CYLINDER WIDTH.

AU - Bell, Jonathan

AU - Cosner, George

PY - 1987/6

Y1 - 1987/6

N2 - For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.

AB - For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.

UR - http://www.scopus.com/inward/record.url?scp=0023366144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023366144&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023366144

VL - 47

SP - 534

EP - 543

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -