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arXiv · 2303.05859

Trends to equilibrium for a nonlocal Fokker-Planck equation

Ferdinando Auricchio·Giuseppe Toscani·Mattia Zanella
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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.

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Ferdinando Auricchio, Giuseppe Toscani, Mattia Zanella. 2023-03-10. Trends to equilibrium for a nonlocal Fokker-Planck equation. https://arxiv.org/abs/2303.05859

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