Existence and non-existence of transition fronts in mixed ignition-monostable media. (16th January 2018)

• Record Type: Journal Article
• Authors: Graham, Cole; Shean Lim, Tau; Ma, Andrew; Weber, David
• Is Part Of: Nonlinearity. Volume 31:Number 2(2018:Feb.)
• Page Start: 651
• Page End: 666
• Publication Date: 2018-01-16
• Subjects: reaction–diffusion equations -- transition fronts -- mixed ignition-monostable reactions; 35K57 -- 35C07 (Partial differential equations); Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa952c
• Languages: English
• ISSNs: 0951-7715

Abstract

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.