## Abstract

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c ≥ 2δ in the F-KPP equation.

Original language | English |
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Pages (from-to) | 36-51 |

Number of pages | 16 |

Journal | Mathematical Biosciences |

Volume | 266 |

DOIs | |

Publication status | Published - Aug 2015 |

Externally published | Yes |

## Keywords

- Evans functions
- Fisher-KPP equation
- Keller-segel equations
- Spectral stability
- Travelling waves