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arXiv · 1311.7206

Transition fronts for inhomogeneous monostable reaction-diffusion equations via linearization at zero

Tianyu Tao·Beite Zhu·Andrej Zlatos
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Abstract

We prove existence of transition fronts for a large class of reaction-diffusion equations in one dimension, with inhomogeneous monostable reactions. We construct these as perturbations of corresponding front-like solutions to the linearization of the PDE at $u=0$. While a close relationship of the solutions to the two PDEs has been well known and exploited for KPP reactions (and our method is an extension of such ideas from [15]), to the best of our knowledge this is the first time such an approach has been used in the construction and study of fronts for non-KPP monostable reactions.

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Tianyu Tao, Beite Zhu, Andrej Zlatos. 2013-11-28. Transition fronts for inhomogeneous monostable reaction-diffusion equations via linearization at zero. https://doi.org/10.1088/0951-7715%2F27%2F9%2F2409

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