Numerical computation of an evans function for travelling waves

K. Harley, P. Van Heijster, R. Marangell*, G.J. Pettet, M. Wechselberger

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)36-51
Number of pages16
JournalMathematical Biosciences
Volume266
DOIs
Publication statusPublished - Aug 2015
Externally publishedYes

Keywords

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

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