Asymptotics of the solution to the mixed problem for the kinetic equation of neutron transport
type: Item
instance of: scholarly article
title: Asymptotics of the solution to the mixed problem for the kinetic equation of neutron transport
zbMATH Open document ID: 0882.45010
published in: Doklady Mathematics
publication date: 1997-08-20T00:00:00Z
review text: The asymptotic behaviour of the kinetic equation of neutron transport is considered. The coefficient \(\sigma(v,r)\) (the collision probability per unit of the path length) depends on the neutron velocity \(v\) and the space variable \(r\in D\). The asymptotics of the solution is analysed on the small parameter \(h=(\sigma_0 d)^{-1}\), where \(\sigma_0= \min\sigma(v,r)\), \(d=\text{diam}(D)\). This problem is divided into two cases: the coefficients of equation change smoothly (fluently) or they are rapidly oscillating. The conditions of the main results are expressed by the spectrum of the operator-valued symbol of the modified kinetic equation operator. Then the resolvent of that operator tends to zero, when special conditions are fulfilled.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 82C70
zbMATH DE Number: 1050687
zbMATH Keywords: kinetic equation
zbMATH Keywords: neutron transport
zbMATH Keywords: asymptotics
zbMATH Keywords: spectrum
zbMATH Keywords: symbol
zbMATH Keywords: resolvent
author: Valeri V. Kucherenko
reviewed by: Stanislav Míka
MaRDI profile type: Publication
Recommended article: Asymptotics of the solution to the singularly perturbed nonstationary neutron transport equation
Recommended article: Q3361384
Recommended article: Asymptotic analysis of unsteady neutron transport equation
Recommended article: Q4297926
Recommended article: Q5185504
Recommended article: Q3320903
Recommended article: Q3682994
Recommended article: Q3726736
Recommended article: Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport
Recommended article: Q4350314
description: scientific article; zbMATH DE number 1050687