On existence of semi-wavefronts for a non-local reaction-diffusion equations with distributed time delay

Abstract

We establish the existence of semi-wavefronts solutions for a non-local delayed reaction-diffusion equation with monostable nonlinearity. The existence result is proved for all speeds $c\ge c_{\star }$, where the determination of $c_{\star }$ is similar to the calculation of the minimal speed of propagation. The results are applied to some non-local reaction-diffusion epidemic and population models with distributed time delay.

arXiv comment19 pages, 2 figures. arXiv admin note: text overlap with arXiv:1309.4376