Admissible speeds of transition fronts for nonautonomous monostable equations

Abstract

We consider a reaction-diffusion equation with a nonlinear term of the Fisher-KPP-type, depending on time $t$ and admitting two limits as $t\to\pm\infty$. We derive the set of admissible asymptotic past and future speeds of transition fronts for such an equation. We further show that any transition front which is noncritical as $t\to-\infty$ always admits two asymptotic past and future speeds. We finally describe the asymptotic profiles of the noncritical fronts as $t\to\pm\infty$.