Speaker
Description
In this talk, I will consider nonhomogeneous kinetic equations that involve a free transport operator and a diffusion of porous medium type acting on velocities. The main novelty is a gradient flow interpretation of dynamics driven by an interplay of conservative and dissipative effects. Relying on a notion of discrepancy adapted to a phase space of positions and velocities, built upon second-order characteristics obeying Newton's laws, I will explain that the equation appears as the steepest descent of the free energy functional. I will also prove that approximate solutions constructed with an implicit Euler à la JKO scheme converge to a solution of the kinetic nonlinear equation. This is based on a recent joint work with Giovanni Brigati, Jean Dolbeault and Filippo Quattrocchi.