Hyperballistic Superdiffusion and Explosive Solutions to the Non-Linear Diffusion Equation - Flekkøy, Eirik G.; Hansen, Alex; Baldelli, Beatrice (Frontiers in Physics, 2021)
By means of a particle model that includes interactions only via the local particle concentration, we show that hyperballistic diffusion may result. This is done by findng the exact solution of the corresponding non-linear diffusion equation, as well as by particle simulations. The connection between these levels of description is provided by the Fokker-Planck equation describing the particle dynamics.