Davidson, F.A., Sleeman, B.D. and Crawford, J.W. (1997) Travelling waves in a reaction-diffusion system modelling fungal mycelia. IMA Journal of Applied Mathematics, 58(3), pp. 237-257. (doi: 10.1093/imamat/58.3.237)
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Abstract
We discuss travelling-wave solutions of a system of coupled reaction—diffusion equations used by the authors to describe the macroscopic behaviour of fungal mycelia. Such systems have been used in a multitude of applications; and, in particular, Merkin and Needham (1990, Proc. R. Soc. Lond. A 430, 315–45) have studied a certain formulation as a model for generic isothermal chemical reactions. We show that an alternative analysis provides more complete results in ascertaining the conditions under which travelling-wave solutions exist and that it allows a wider range of parameter values to be considered; this is essential to the application considered in the present case. Numerical investigations of travelling-wave solutions and the related initial-value problem are included to motivate and extend the analysis.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Crawford, Professor John |
Authors: | Davidson, F.A., Sleeman, B.D., and Crawford, J.W. |
College/School: | College of Social Sciences > Adam Smith Business School > Management |
Journal Name: | IMA Journal of Applied Mathematics |
Publisher: | Oxford University Press |
ISSN: | 0272-4960 |
ISSN (Online): | 1464-3634 |
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