Yuming Paul Zhang, UCSD

Abstract. We study the reaction-fractional-diffusion equation $u_t+(-\Delta)^s u=f(u)$ with ignition and monostable reactions $f$, and $s\in (0,1)$. We obtain the first optimal bounds on the propagation of front-like solutions in the cases where no traveling fronts exist. Our results cover most of these cases, and also apply to propagation from localized initial data. This is a joint work with A. Zlatos.