# American Institute of Mathematical Sciences

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December  2017, 10(4): 1163-1203. doi: 10.3934/krm.2017045

## Diffusive limit with geometric correction of unsteady neutron transport equation

 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Received  October 2015 Revised  November 2016 Published  March 2017

We consider the diffusive limit of an unsteady neutron transportequation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory in [1] which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

Citation: Lei Wu. Diffusive limit with geometric correction of unsteady neutron transport equation. Kinetic & Related Models, 2017, 10 (4) : 1163-1203. doi: 10.3934/krm.2017045
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##### References:
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