Zu Chongzhi Center Mathematics Research Seminar

Date and Time(China standard time): Monday, September 19, 8:00-9:00pm

Zoom ID: 934 4541 5034

Passcode: dkumath

Title: Optimal Estimates on the Propagation of Reactions with Fractional Diffusion

Speaker: Yuming Zhang

Bio: Yuming Zhang got his PhD from University of California, Los Angeles in 2019. He is currently an assistant professor at Auburn University. He works on partial differential equations. More precisely, he is interested in stochastic homogenization, reaction-diffusion equations, free boundary problems, regularity problems, and optimal transport.

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 joint work with Andrej Zlatos.