Transition fronts for the Fisher-KPP equation

Francois Hamel (1) , Luca Rossi (2)

1 I2M - Institut de Mathématiques de Marseille
2 Dipartimento di Matematica [padova]

This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the class of transition fronts is much larger and the dynamics of the solutions of such equations is very rich. In the paper, we describe the class of transition fronts and we study their qualitative dynamical properties. In particular, we characterize the set of their admissible asymptotic past and future speeds and their asymptotic profiles and we show that the transition fronts can only accelerate. We also classify the transition fronts in the class of measurable superpositions of standard traveling fronts.

Mots clés: Reaction-diffusion equations; Fisher-KPP equation; speeds; transition fronts

Domaines: Equations aux dérivées partielles [math.AP]

Francois Hamel, Luca Rossi. Transition fronts for the Fisher-KPP equation. Transactions of the American Mathematical Society, 2016, 368, pp.8675-8713. ⟨hal-00976638v2⟩