Travelling front solutions of a nonlocal Fisher equation
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- 1 September 2000
- journal article
- research article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 41 (3) , 272-284
- https://doi.org/10.1007/s002850000047
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
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