Publications [#287352] of James H. Nolen

Papers Published

1. Nolen, J; Roquejoffre, JM; Ryzhik, L; Zlatoš, A, Existence and Non-Existence of Fisher-KPP Transition Fronts, Archive for Rational Mechanics and Analysis, vol. 203 no. 1 (2012), pp. 217-246, Springer Nature, ISSN 0003-9527 [2392], [doi]
   (last updated on 2024/04/15)

   Abstract:
   We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global-in-time solutions while creating a global-in-time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized inhomogeneity leads to the existence of transition fronts, but only in a finite range of speeds. These results are in contrast with both Fisher-KPP reactions in homogeneous media as well as ignition-type reactions in inhomogeneous media. © 2011 Springer-Verlag.