Existence and BV-regularity for Neutron transport equation in non-convex domain

Abstract

This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by $L^2-L^{\infty }$ method, which was established to study Boltzmann equation in \cite{[Guo2]}. Based on the uniform estimates of the solution, we also consider the BV-regularity of the solution in non-convex domain. A cut-off function, which aims to exclude all the characteristics emanating from the grazing set ${\mathfrak{S}}_B$, has been constructed precisely.

50 pages. arXiv admin note: text overlap with arXiv:1409.0160