Numerical computation of an Evans function for travelling waves

Harley, K., van Heijster, P., Marangell, R., Pettet, G.J., & Wechselberger, M. (2015) Numerical computation of an Evans function for travelling waves. Mathematical Biosciences, 266, pp. 36-51.

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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≥sqrt(2δ) in the F-KPP equation.

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ID Code: 85919
Item Type: Journal Article
Refereed: Yes
DOI: 10.1016/j.mbs.2015.05.009
ISSN: 0025-5564
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 Elsevier
Copyright Statement: Licensed under the Creative Commons Attribution; Non-Commercial; No-Derivatives 4.0 International. DOI: 10.1016/j.mbs.2015.05.009
Deposited On: 23 Jul 2015 00:49
Last Modified: 24 Sep 2016 04:15

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