Pushed, pulled and pushmi-pullyu fronts of the Burgers-Fisher-KPP equation

Abstract: We consider the long time behavior of the solutions to the Burgers-Fisher-KPP equation. This equation exhibits a transition from the pulled (a la FKPP)  to the pushed (a la Allen-Cahn) behavior at a critical value $\beta_c$ of the strength of the Burgers term. The main interest is in the analysis of the pushmi-pullyu stage at $\beta=\beta_c$. This is a joint work with J. An and C. Henderson.