Stability of Stationary Transport Equations with Accretive Collision Operators

Abstract

In this paper we consider transport equations with accretive collision operators. We characterize when the equation has a unique solution and show that in this case the solution is stable under small perturbations of the collision operator and the initial value. In one case in which there is more than one solution we show how to make a special selection of a solution, which is then stable again under small perturbations of both the collision operator and the initial value. The results obtained here parallel those obtained earlier for the case where the collision operator is positive semidefinite. © 2000 Academic Press.