On existence of solutions for Boltzmann Continuous Slowing Down transport equation

Abstract

The paper considers a linear Boltzmann transport equation (BTE), and its Continuous Slowing Down Approximation (CSDA). These equations are used to model the transport of particles e.g. in dose calculation of radiation therapy. We prove the existence and uniqueness of weak solutions, under sufficient criteria and in appropriate L2-based spaces, of a single (particle) CSDA-equation by using the theory of m-dissipative operators. Relevant a priori estimates are shown as well. In addition, we prove the corresponding results and estimates for a system of coupled transport equations. We also outline a related inverse problem.