KPP reaction-diffusion equations with a non-linear loss inside a cylinder
Abstract
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
Cite
@article{arxiv.1004.2955,
title = {KPP reaction-diffusion equations with a non-linear loss inside a cylinder},
author = {Thomas Giletti},
journal= {arXiv preprint arXiv:1004.2955},
year = {2015}
}