*Constantin Eichenberg (University of Bonn (Germany))*

#### Abstract

Coarsening, usually associated with the perpetuated growth of a systemâ€™s geometric length scale, is an ubiquitous phenomenon in nature. In material science it can be observed in the phase separation of alloys, formation of droplets in thin films or the growth of polycristalline structures, while also occurring in stochastic particle systems such as the zero-range process. The typical problem is to characterize generic dynamical properties, such as coarsening rates or self-similarity, for a large class of initial configurations. Heuristic considerations, simulations and experiments often give a rough picture, whereas the rigorous mathematical description remains a challenge. In this talk, I will consider a class of toy models for coarsening on a one dimensional infinite lattice, where sites transfer mass via nonlinear backward diffusion and empty sites vanish from the system. While simple, this system already exhibits interesting dynamical properties. I will discuss the existence of initial configurations for which the system coarsens at the expected rate, but in a very organised way. The idea is to analyse the time-reversed evolution and make use of the parabolic theory of De Giorgi, Nash and Moser in the spatially discrete setting.