English

On regularity of solutions for certain linear Boltzmann transport equations

Analysis of PDEs 2024-09-04 v5

Abstract

The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their collision terms. Hyper-singular integrals can be approximated by partial differential operators together with partial integral operators which leads to an approximation under consideration. This type of approximation is applied, for example in the dose calculation of radiation therapy. The related transport problem is a characteristic initial inflow boundary value problem. Regularity results of solutions are verified utilizing the scales of relevant anisotropic Sobolev spaces.

Keywords

Cite

@article{arxiv.2102.08008,
  title  = {On regularity of solutions for certain linear Boltzmann transport equations},
  author = {Jouko Tervo},
  journal= {arXiv preprint arXiv:2102.08008},
  year   = {2024}
}

Comments

list of keywords supplemented, some details clarified, supplemented references, added subsection 5.3, improved and corrected some technicalities, added section 7, some changes/corrections to section 6.3 made, some typos corrected

R2 v1 2026-06-23T23:12:05.441Z