Dowan Koo

A gradient flow for the porous medium equations with Dirichlet boundary conditions

We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy functional with respect to W b 2 distance, wh...

Hydrodynamic Limit from Kinetic Models with Massless Electrons to the Ionic Euler–Poisson System

Abstract. 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 coupled with either a nonlinear Fokker–Planck operator or a local alignment term. In both kine...