Travelling wave solutions in a negative nonlinear diffusion-reaction model.

We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion-reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, [Formula: see text], and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.