Front transition in higher order diffusion equations with a general reaction nonlinearity
by S. Shamseldeen
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 9, No. 3, 2019

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.

Online publication date: Mon, 29-Jul-2019

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