Diffusive limit with geometric correction of unsteady neutron transport equation

Lei Wu

doi:10.3934/krm.2017045

Article Contents

2017, Volume 10, Issue 4: 1163-1203. Doi: 10.3934/krm.2017045

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Diffusive limit with geometric correction of unsteady neutron transport equation

Lei Wu

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

Received: September 30, 2015

Revised: October 31, 2016

Published: November 2017

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Abstract

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.

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Mathematics Subject Classification: 35L65, 82B40, 34E05.

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References

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