Existence and non-existence of transition fronts in mixed ignition-monostable media. (16th January 2018) - Graham, Cole; Shean Lim, Tau; Ma, Andrew; Weber, David
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 the results and methods introduced in Nolen et al 2012 ( Arch. Ration. Mech. Anal . 203 217–46), which studied the same question in inhomogeneous KPP media.