Numerical computation of an Evans function for travelling waves
| Autor: | Harley, K., Heijster, P. v, Marangell, R., Pettet, G. J., Wechselberger, M. |
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| Rok vydání: | 2013 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $c \geq 2 \sqrt{\delta}$ in the F-KPP equation. Comment: 37 pages, 11 figures |
| Databáze: | arXiv |
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