4 papers
Boundary-compatible interacting approximations of quasilinear PDEs on bounded domains
Thierry Paul, Emmanuel Trélat
We develop a general operator-theoretic route that turns Kato-type quasilinear evolution systems on a Banach scale into finite-dimensional interacting approximations. The c…
Numerical modeling of flocking dynamics with topological interactions
Marta Menci, Thierry Paul, Stefano Rossi +1
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macro…
Multi-agent systems with multiple-wise interaction: Propagation of chaos and macroscopic limit
Thierry Paul, Stefano Rossi, Emmanuel Trélat
We consider interacting multi-agent systems where the interaction is not only pairwise but involves simultaneous interactions among multiple agents (multiple-wise interaction). By…
Universal approximations of quasilinear PDEs by finite distinguishable particle systems
Thierry Paul, Emmanuel Trélat
In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ).…