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.
Original language | English |
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Pages (from-to) | 237-257 |
Number of pages | 21 |
Journal | IMA Journal of Applied Mathematics |
Volume | 58 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jun 1997 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics