Investigation of the stability of Boltzmann's collision equation by a family of Lyapunov functionals

For Boltzmann's equation a continuous family of Lyapunov functionals (entropy-like functionals) is established which imply under suitable boundary conditions uniform equi-boundedness of the solutions and (uniform) asymptotic stability in the large and integral stability of the equilibrium solution. Boltzmann's H-functional is shown to be an element of this family.