AUTHOR=Flekkøy Eirik G. , Hansen Alex , Baldelli Beatrice 

TITLE=Hyperballistic Superdiffusion and Explosive Solutions to the Non-Linear Diffusion Equation

JOURNAL=Frontiers in Physics

VOLUME=9

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.640560

DOI=10.3389/fphy.2021.640560

ISSN=2296-424X

ABSTRACT=<p>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. PACS numbers:</p>