Coarse graining of a Fokker-Planck equation with excluded volume effects preserving the gradient flow structure - Bruna, M.; Burger, Martin; Carrillo, J. A. (European Journal of Applied Mathematics, 2020)
The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper, we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion or short-range repulsive potentials.We formulate the microscopic model as a high-dimensional gradient flow in the Wasserstein metric for an appropriate free-energy functional. Then we use the JKO approach to identify the asymptotics of the metric and the freeenergy functional beyond the lowest order for single particle densities in the limit of small particle volumes by matched asymptotic expansions. While we use a propagation of chaos assumption at far distances, we consider correlations at small distance in the expansion. In this way, we obtain a clear picture of the emergence of a macroscopic gradient structure incorporating corrections in the free-energy functional due to the volume exclusion.
CRIS-Team Scopus Importer:2020-10-23
Keywords: Asymptotic expansions; Fokker-Planck equations; Variational methods; Volume exclusion