Trends to equilibrium for a nonlocal Fokker-Planck equation
Analysis of PDEs
2023-06-06 v2 Adaptation and Self-Organizing Systems
Abstract
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance, towards the steady profile characterized by uniform spreading over a finite interval of the line. The result follows by combining entropy methods for quantifying the decay of the solution towards its quasi-stationary distribution, with the properties of the quasi-stationary profile.
Keywords
Cite
@article{arxiv.2303.05859,
title = {Trends to equilibrium for a nonlocal Fokker-Planck equation},
author = {Ferdinando Auricchio and Giuseppe Toscani and Mattia Zanella},
journal= {arXiv preprint arXiv:2303.05859},
year = {2023}
}