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IMA Journal of Applied Mathematics Advance Access published online on March 28, 2008
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxn007
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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.

Wavefronts for a non-local reaction–diffusion population model with general distributive maturity

Peixuan Weng{dagger}

School of Mathematics, South China Normal University, Guangzhou 510631, People's Republic of China

Jianhong Wu{ddagger}

Center for Disease Modeling, Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada

{dagger} Email: wengpx{at}scnu.edu.cn

{ddagger} Email: wujh{at}yorku.ca

Received on August 18, 2006; Revision received November 17, 2007. Accepted on January 16, 2008

We consider the Al-Omari and Gourley non-local reaction–diffusion population model with distributed maturity. Existence of monotone wavefronts for some particular probability distribution of maturity that permits the linear chain trick was previously obtained; here, we consider the most general form of such a distribution using some comparison arguments for abstract functional differential equations with infinite delay and a fixed point approach combined with the upper and lower solutions technique.

Keywords: non-local distribution; reaction–diffusion equation; infinite distributed maturity; monotone travelling front.


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