Search results for "trend to equilibrium."

The dissipative linear Boltzmann equation for hard spheres

2005

The authors prove existence and uniqueness of a Maxwellian, normalized equilibrium state for a dissipative linear Boltzmann equation with hard-sphere collision kernel modeling a granular gas and, for initial data with finite temperature and entropy, strong L 1 convergence (obtained through compactness arguments) toward the equilibrium of the solutions in the space-homogeneous case. The form of the equilibrium state, which is universal for the family of collision operators including hard, soft and Maxwellian interactions, is guessed through a grazing collision asymptotics and then proved to be the equilibrium state through Fourier analysis. Uniqueness and strong L 1 convergence proofs follow…