article

Title: Lyapunov functionals for the Enskog-Boltzmann equation

Authors: Seung Yeal Ha

Issue: Volume 54 (2005), Issue 4, 997-1014

Abstract:

$We present two Lyapunov functionals measuring future interactions between particles with different velocities, and $L^1$-distance between two classical solutions for the Enskog-\linebreak[4] Boltzmann equation, when initial datum is a small perturbation of a vacuum and tends to zero fast enough at infinity in the phase space. These Lyapunov functionals yield time-asymptotic convergence of classical solutions to the collision free motion and the $L^1$ stability of classical solutions.$