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.
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Received: 8 August 1999 / Revised: 3 March 2000 / Published online: 14 September 2000
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Gourley, S. Travelling front solutions of a nonlocal Fisher equation. J Math Biol 41, 272–284 (2000). https://doi.org/10.1007/s002850000047
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DOI: https://doi.org/10.1007/s002850000047