Deterministic Particle Approximation of Porous Medium Equations

par Charles Elbar (ICJ)

mercredi 19 févr. 2025, 10:00 → 11:30 Europe/Paris

112 (Braconnier)

Consider a system of particles where the motion is given by a set of ODEs. The empirical measure, which is the sum of the Dirac masses, satisfies a non-local PDE. By sending the range of the interaction kernel among particles to zero, we recover the porous medium equation in the limit. This reasoning provides a deterministic (i.e., non-stochastic) particle approximation of the porous medium equation. In this talk, we present how to study the limit from non-local to local. The argument is based on the works of Lions and Mas-Gallic for quadratic nonlinearity, as well as Carrillo, Esposito, and Wu for more general nonlinearities. Lastly, we present an ongoing work on the convergence rate in one dimension for a specific interaction kernel.