Weekly Seminar
Impact of interaction forces in first order many-agent systems for swarm manufacturing
Mattia Zanella (University of Pavia (Italy))
Thu, 18 Jan 2024 • 10:00 coffee/tea in 001 // 10:30-11:30 talk in 008 • Pontdriesch 14, room 008 SeMath (host: Michael Herty)

Abstract

We study equilibration rates for nonlocal Fokker-Planck equations arising in swarm manufacturing. The PDEs of interest are characterised by a time-dependent nonlocal diffusion coefficient and a nonlocal drift, modeling the relaxation of a large swarms of agents, feeling each other in terms of their distance, towards the steady profile characterized by a uniform spreading over a domain. 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.

Bibliography: [1] F. Auricchio, G. Toscani, M. Zanella. Trends to equilibrium for a nonlocal Fokker-Planck equation. Applied Mathematics Letters, 145: 108746, 2023. [2] F. Auricchio, G. Toscani, M. Zanella. Fokker-Planck modeling of many-agent systems in swarm manufacturing: asymptotic analysis and numerical results. Communications in Mathematical Sciences, 21(6):1655-1677, 2023.