On Global Existence and Regularity of Solutions for a Transport Problem Related to Charged Particles

Abstract The paper considers a class of linear Boltzmann transport equations which models charged particle transport, for example in dose calculation of radiation therapy. The equation is an approximation of the exact transport equation containing hyper-singular integrals in its collision terms. The paper confines to the global case where the spatial domain G is the whole space Existence results of solutions for the due initial value problem are formulated by applying variational methods. In addition, some regularity results of solutions are verified in scales of relevant anisotropic mixed-norm Sobolev spaces.