Title: Front transition in higher order diffusion equations with a general reaction nonlinearity

Authors: S. Shamseldeen

Addresses: Faculty of Engineering, Mathematics and Engineering Physics Department, Mansoura University Mansoura 35516, Egypt

Abstract: In this paper, we investigate the wave front solutions of a class of higher order reaction diffusion equations with a general reaction nonlinearity. Linear stability analysis with a modulated travelling wave perturbation is used to prove the existence of wave front solutions. We proved that the studied equation supports both monotonic translating front and patterned front solutions. Also, a minimal front speed and the condition for a transition between these front types (monotonic and patterned) are determined. Two numerical examples are discussed (the extended Fisher-Kolmogorov equation with two different reaction nonlinearities) to support the obtained results.

Keywords: reaction diffusion equations; travelling waves; Minimal front speed; pulled fronts.

DOI: 10.1504/IJDSDE.2019.101216

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.3, pp.225 - 233

Received: 26 Oct 2017
Accepted: 07 Feb 2018

Published online: 29 Jul 2019 *

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