Publication 16-CNA-003

Asymptotic Analysis Of Transport Equation In Annulus

Lei Wu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
lwu2@andrew.cmu.edu

Xiongfeng Yang
Department of Mathematics, MOE-LSC and SHL-MAC
Shanghai Jiao Tong University
Shanghai, 200240, P.R. China
xf-yang@sjtu.edu.cn

Yan Guo
Division of Applied Mathematics
Brown University
Providence, RI 02912, USA
guoy@dam.brown.edu

Abstract: We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem in [1] states that the solution can be approximated in $L^\infty$ by the leading order interior solution plus the corresponding Knudsen layers in the diffusive limit. In this paper, we construct a counterexample of this result via a different boundary layer expansion with geometric correction.

Get the paper in its entirety as  16-CNA-003.pdf

---

«   Back to CNA Publications