​Accelerating propagation in diffusion phenomena

In this talk, we focus on the accelerating propagation in diffusion phenomena. It is well-known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is light-tailed and propagates by accelerating when the kernel has a heavy-tail. However, in such systems, we find that one species can propagate by accelerating although its dispersal kernel is lighttailed, which is a new and interesting phenomenon. In particular, the accelerating phenomenon also has been found in nonlocal free boundary problems and in shifting environments.