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, c ∗ , and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions. [ABSTRACT FROM AUTHOR]