2014/04/10 by François Hamel, Luca Rossi, Hamel, Francois +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1404.2821
openalex publication_date 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.