Asymptotic Behavior of Degenerate Linear Kinetic Equations with Non-Isothermal Boundary Conditions
We study the degenerate linear Boltzmann equation inside a bounded domain with the Maxwell and the Cercignani-Lampis boundary conditions, two generalizations of the diffuse reflection, with variable temperature. We prove for the first time the existence of a steady state and a rate of convergence towards it without assumptions on the temperature variations.
Feb 1, 2024
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