From the 1 of 9 linked papers with an AI index.
9 papers
Conditional hypocoercivity for nonlinear kinetic Fokker--Planck equations
Jose A. Carrillo, Dowan Koo, Sihyun Song
The paper studies how solutions of nonlinear kinetic Fokker–Planck equations with porous‑medium diffusion approach equilibrium over time, proving exponential convergence in L¹ unde…
Weakly inhomogeneous solutions to a nonlinear Vlasov--Fokker--Planck equation in a domain
Sihyun Song
A nonlinear Vlasov--Fokker--Planck equation is considered in a bounded domain, with specular reflection imposed on the boundary. It is proven that if the initial datum is sufficien…
A modified Consensus-Based Optimization model: consensus formation and uniform-in-time propagation of chaos
Young-Pil Choi, Seungchan Lee, Sihyun Song
We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation…
Global weak solutions to nonlinear kinetic Fokker--Planck equations in bounded domains under physical initial data
Young-Pil Choi, Sihyun Song
We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection b…
Hydrodynamic limit from kinetic models with massless electrons to the ionic Euler--Poisson system
Young-Pil Choi, Dowan Koo, Sihyun Song
We study the derivation of ion dynamics, namely, the ionic Euler--Poisson system, from kinetic descriptions. The kinetic framework consists of the ionic Vlasov--Poisson equation co…
Micro-macro and macro-macro limits for controlled leader-follower systems
Giacomo Albi, Young-Pil Choi, Matteo Piu +1
We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system co…