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Journal of Mathematical Biology

, Volume 41, Issue 3, pp 272–284 | Cite as

Travelling front solutions of a nonlocal Fisher equation

  • S.A. Gourley

Abstract.

We consider a scalar reaction-diffusion equation containing a nonlocal term (an integral convolution in space) of which Fisher‘s equation is a particular case. We consider travelling wavefront solutions connecting the two uniform states of the equation. We show that if the nonlocality is sufficiently weak in a certain sense then such travelling fronts exist. We also construct expressions for the front and its evolution from initial data, showing that the main difference between our front and that of Fisher‘s equation is that for sufficiently strong nonlocality our front is non-monotone and has a very prominent hump.

Keywords

Initial Data Uniform State Front Solution Nonlocal Term Fisher Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • S.A. Gourley
    • 1
  1. 1.Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 5XH, UK. e-mail: s.gourley@mcs.surrey.ac.ukGB

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