Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our approach allows us to treat general domains with all types of boundary conditions (including the specular reflection boundary condition) in a unified framework.
Jul 13, 2022
A coupling approach for the convergence to equilibrium for a collisionless gas
This article was part of my PhD thesis, advised by Nicolas and Stéphane Mischler. You can find Nicolas’ webpage here.
Apr 1, 2022
Convergence toward the steady state of a collisionless gas with Cercignani–Lampis boundary condition
This article is the starting point of my project focusing on the Cercignani-Lampis boundary condition in kinetic theory. You might also want to check the related preprint Asymptotic Behavior of Degenerate Linear Kinetic Equations with Non-Isothermal Boundary Conditions, where I consider collisional models with the same boundary conditions.
Mar 1, 2022
Long-Time Behavior of Kinetic Equations with Boundary Effects
This is the manuscript of my PhD thesis. Some slides are also available, from which the image above, taken from the simulation of the evolution of 5000 particles in a star-shaped domain following a free-transport evolution with boundary effects, is extracted (I advise to open the pdf with Adobe, as embedded simulations work better there).
Dec 18, 2020
A semigroup approach to the convergence rate of a collisionless gas
This article was part of my PhD thesis.
Nov 1, 2020