| Abstract: |
| In this talk, we present the derivation of macroscopic models of non-local consensus and relaxation dynamics in interacting multi-agent systems as hydrodynamic limits of Povzner-Boltzmann-type kinetic equations. First, we show that relaxation dynamics are well described, at the macroscopic scale, by first-order conservation laws with non-local flux. Next, we prove that consensus dynamics can instead be approximated macroscopically by a class of second-order models reminiscent of the celebrated Aw-Rascle-Zhang system of conservation laws for vehicular traffic, at least when the non-locality of the interactions is sufficiently small. We also visualise numerically the correspondence between the solutions to the stochastic particle models underlying the kinetic description and their macroscopic limits. |
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