Travelling waves and instability in a Fisher–KPP problem with a nonlinear advection and a high-order diffusion
Universidad Francisco de Vitoria Escuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223, Pozuelo de Alarcón, Madrid, Spain
Accepted: 19 July 2021
Published online: 26 July 2021
The instability of travelling waves (TW) in high-order operators has been a source of investigation in the last years. Instability shall be understood as the existence of oscillatory exponential bundles of solutions. One of the principal topics to explore is related with the characterization of the mentioned instability phenomena in the proximity of the stationary solutions given by KPP-Fisher terms. Along this analysis, the main areas discussed cover TW instability, TW propagation speed and characterization of a local inner region with positive monotone behaviour of solutions (also called positive inner region). Furthermore, a sharp estimation of the TW propagation speed to ensure the existence of such positive inner region is obtained. Eventually, insights on regularity, existence and uniqueness of solutions are provided as supplementary information.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021