Diffusive limit with geometric correction of unsteady neutron transport equation
Copyright policy )Diffusive limit with geometric correction of unsteady neutron transport equation
We consider the diffusive limit of an unsteady neutron transport equation 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 \cite{Bensoussan.Lions.Papanicolaou1979} which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.
34 pages. arXiv admin note: substantial text overlap with arXiv:1404.2583
- Carnegie Mellon University United States
compatibility condition, diffusive limit, Mathematics - Analysis of PDEs, Hyperbolic conservation laws, FOS: Mathematics, Kinetic theory of gases in equilibrium statistical mechanics, \(\epsilon\)-Milne problem, Knudsen layer, Asymptotic expansions of solutions to ordinary differential equations, Singular perturbations in context of PDEs, Analysis of PDEs (math.AP)
compatibility condition, diffusive limit, Mathematics - Analysis of PDEs, Hyperbolic conservation laws, FOS: Mathematics, Kinetic theory of gases in equilibrium statistical mechanics, \(\epsilon\)-Milne problem, Knudsen layer, Asymptotic expansions of solutions to ordinary differential equations, Singular perturbations in context of PDEs, Analysis of PDEs (math.AP)
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