Global solutions of nonstationary kinetic equations

For the nonstationary Boltzmann equation $$\frac{{\partial F}}{{\partial t}} + \xi _d \frac{{\partial F}}{{\partial x_d }} = Q(F,F),t > 0,\xi \in R^3 ,x \in \Omega \subset R^3 ,$$ one proves the unique global solvability of the Cauchy problem under nondifferentiable initial data and the unique global solvability of initial-boundary-value problems with homogeneous boundary conditions; it is shown that the solutions of the initial-boundary-value problems decay exponentially as t → ∞.