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arXiv · 1004.2955

KPP reaction-diffusion equations with a non-linear loss inside a cylinder

Thomas Giletti
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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.

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Thomas Giletti. 2010-04-17. KPP reaction-diffusion equations with a non-linear loss inside a cylinder. https://doi.org/10.1088/0951-7715%2F23%2F9%2F012

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