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arXiv · 1603.04975

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

Yan Guo·Xiongfeng Yang
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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.

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Yan Guo, Xiongfeng Yang. 2016-03-16. Existence and BV-regularity for Neutron transport equation in non-convex domain. https://arxiv.org/abs/1603.04975

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