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The existence of travelling plane waves in a general class of competition-diffusion systems |
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JH van Vuuren1 & J Norbury1
Abstract
It is shown that a one-parameter family of positive, uniformly bounded, monotonic travelling plane wave solutions of a multi-component system of nonlinear, diagonally convex competition-diffusion equations exists if and only if the wave speed is taken greater to or equal than a certain lower bound, which is a function of the reaction terms and diffusion coefficients of the system.
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Affiliations
1 Mathematical Institute, University of Oxford, 24-29 St Giles', OX1 3LB, United Kingdom, email: ecmigb@vax.ox.ac.uk