Initial-boundary value problems of the Boltzmann equation at zero temperature

Abstract

For a general class of collision operators, we show that the stationary boundary valve problem of the one dimensional linear Boltzmann equation on a finite intcrvall including an arbitrarily high constant external force can be solved analytically (apart form an inverse Laplace transform) at zero temperature of the host medium. As a byproduct we obtain existence, positivity and uniqueness of the solution. Our method also applies to coupled initial-boundary value problems, for which we demonstrate the decay to the solution of the stationary boundary value problem.