Transition fronts for the Fisher-KPP equation (Q2822716)

This paper is concerned with transition fronts for reaction-diffusion equations of Fisher-KPP type. The difference between standard traveling fronts and transition fronts is clearly presented and basic examples of transition fronts connecting the unstable steady state to the stable one are presented. The authors describe the class of transition fronts and study their qualitative dynamical properties, characterizing their asymptotic propagation rates for large negative and positive times, and describing their asymptotic profiles. In particular, they characterize the set of admissible asymptotic past and future speeds and their asymptotic profiles and show that the transition fronts can only accelerate, but cannot move infinitely fast. Important notions associated with the transition fronts, for instance, those related with their propagation speeds, are given. A characterization of transition fronts and their asymptotic past and future speeds is presented. A notion of solution to the former equation associated with a nonnegative Borel measure is presented. They classify the transition fronts in the class of measurable superpositions of standard traveling fronts. Several cases are discussed, including heterogeneous reaction-diffusion equations.