Bifurcating solutions and stabilities for multigroup neutron fission systems with temperature feedback
type: Item
instance of: scholarly article
title: Bifurcating solutions and stabilities for multigroup neutron fission systems with temperature feedback
zbMATH Open document ID: 0848.35058
author: Anthony W. Leung
author: Luis A. Ortega
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-03-24T00:00:00Z
review text: The following reaction-diffusion system describing neutron fission in a reactor is studied: \hskip17mm \(\Delta u_i(x)+ \sum^m_{j= 1} H_{ij} (x, V(x)) u_j(x)= 0\text{ for all } x\in k\Omega,\;i= 1,\dots, m\), \hskip17mm \(\Delta V(x)- c(x) V(x)+ \sum^m_{j= 1} g_j(x) u_j(x)= 0\text{ for all } x\in k \Omega\), \hskip17mm \(u_i(x)= V(x)= 0\text{ for all } x\in \partial k \Omega,\;i= 1,\dots, m\). Here \(\Omega\) is a fixed domain in \(\mathbb{R}^N\), \(k\) is a positive parameter, \(u_i\) describes the neutron flux of the \(i\)th energy group, \(V(x)\) denotes the temperature, \(H_{ij}\) describes the temperature dependent fission and scattering rates of the various energy groups, \(c(x)\) is the cooling function and \(g_j(x)\) describes the rate of temperature increase corresponding to neutrons in the \(j\)th group. It is shown that positive steady states bifurcate from the trivial solution for \(k\) crossing a certain critical \(k_0\). The characterization of this bifurcation point \(k_0\) (i.e. of the critical size of the reactor) is given and the stability of bifurcating solutions is proved.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 859218
zbMATH Keywords: multigroup neutron fission system
reviewed by: Milan Kučera
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1313
OpenAlex ID: W2047298135
DOI: 10.1006/JMAA.1995.1313
Recommended article: Reaction-diffusion systems for multigroup neutron fission with temperature feedback: positive steady-state and stability
Recommended article: Stability analysis of the neutron transport equation with temperature feedback
Recommended article: Nonlinear reactor multigroup neutron transport system: Existence and stability problems
Recommended article: Positive Solutions for Temperature-Dependent Two-Group Neutron Flux Equations: Equilibria and Stabilities
Recommended article: Optimal control of multigroup neutron fission systems
Recommended article: Positive Solutions for Reactor Multigroup Neutron Transport Systems: Criticality Problem
Recommended article: Q5193648
Recommended article: On the Leung-Chen feedback model for nuclear fission
Recommended article: Q5428519
Recommended article: Global stability of the positive equilibrium for a non-cooperative model of nuclear reactors
description: scientific article; zbMATH DE number 859218