STUDY OF THE STABILITY OF THE HOMOGENEOUS BOLTZMANN EQU ATION FOR LATTICE GASES
均匀格子气Boltzmann方程的稳定性研究

The Lyapunov method is applied to finite difference equations in order to study the stability and asymptotic properties of Boltzmann equation of lattice gas. The existence and uniqueness of the equilibrium state are proved. A Lyapunov function can be formed by means of function H that is decreasing and takes its minimum value at the equilibrium state. By the Lyapunov function the stability is Obtained. Moreover, a sufficient condition is provided that makes the function H strictly decrease except at the equilibrium state. The asymptotic stability for homogeneous Boltzmann equation of lattice gas is proved under this condition.