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arXiv · 1705.03563

Existence and non-existence of transition fronts in mixed ignition-monostable media

Cole Graham·Tau Shean Lim·Andrew Ma·David Weber
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Abstract

We study transition fronts for one-dimensional reaction-diffusion equations with compactly perturbed ignition-monostable reactions. We establish an almost sharp condition on reactions which characterizes the existence and non-existence of fronts. In particular, we prove that a strong inhomogeneity in the reaction prevents formation of transition fronts, while a weak inhomogeneity gives rise to a front. Our work extends results and methods introduced by J. Nolen, J.M. Roquejoffre, L. Ryzhik, and A. Zlato\v{s}.

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Cole Graham, Tau Shean Lim, Andrew Ma, David Weber. 2017-05-09. Existence and non-existence of transition fronts in mixed ignition-monostable media. https://doi.org/10.1088/1361-6544%2Faa952c

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