Spectral properties of a streaming operator with diffuse reflection boundary condition
type: Item
instance of: scholarly article
title: Spectral properties of a streaming operator with diffuse reflection boundary condition
zbMATH Open document ID: 0944.47028
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-09-14T00:00:00Z
review text: The author studies the spectrum of a streaming operator with diffuse reflection boundary condition arising in transport theory. This unbounded operator in \(L_1\) is associated with bounded integral operators determined by the boundary condition. The spectrum of the streaming operator is determined by these integral operators. It consist of a countable set of isolated eigenvalues with a finite algebraic multiplicity. Further, the diffuse reflection boundary condition of Maxwell type is considered. In this case the streaming operator has only one real eigenvalue which is simple and all complex eigenvalues have geometrical multiplicity one. A formula for computing these eigenvalues is given and the algebraic multiplicity of complex eigenvalues is discussed.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1354748
zbMATH Keywords: streaming operator
zbMATH Keywords: diffuse reflection boundary conditions
zbMATH Keywords: spectrum
zbMATH Keywords: transport theory
zbMATH Keywords: unbounded operator
zbMATH Keywords: algebraic multiplicity of complex eigenvalues
author: Xianwen Zhang
reviewed by: Milan Kučera
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6494
OpenAlex ID: W1981196457
cites work: Existence and Uniqueness Theorems for the Neutron Transport Equation
cites work: Q4188958
cites work: Q5796557
cites work: Q4148368
cites work: On the spectrum of an unsymmetric operator arising in the transport theory of neutrons
cites work: Q5848524
cites work: Linearized Boltzmann equation in \(L^ 1\) space
cites work: Q3966611
cites work: Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
cites work: A perturbation theorem for the essential spectral radius of strongly continuous semigroups
cites work: Positivity in time dependent linear transport theory
cites work: Spectral properties of the neutron transport equation
cites work: On the spectrum of a one-velocity transport operator with Maxwell boundary condition
DOI: 10.1006/JMAA.1999.6494
description: scientific article; zbMATH DE number 1354748