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IMA Journal of Applied Mathematics Advance Access originally published online on January 14, 2008
IMA Journal of Applied Mathematics 2008 73(1):158-198; doi:10.1093/imamat/hxm059
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The evolution of travelling wave-fronts in a hyperbolic Fisher model. I. The travelling wave theory

D. J. Needham{dagger} and J. A. Leach

School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

{dagger} Email: needham{at}for.mat.bham.ac.uk

In this paper, we consider an initial-value problem for a hyperbolic Fisher equation. In particular, we consider the corresponding travelling wave problem and establish the conditions under which permanent-form travelling wave solutions exist. Numerical simulations of the initial-value problem are also presented.

Keywords: travelling wave-fronts; hyperbolic Fisher model.


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