Boundary value problems in abstract kinetic theory
type: Item
instance of: scholarly article
title: Boundary value problems in abstract kinetic theory
zbMATH Open document ID: 0624.35003
author: William Greenberg
author: C. van der Mee
author: V. Protopopescu
published in: Operator Theory: Advances and Applications
publication date: 1987-01-01T00:00:00Z
review text: This monograph presents a rigorous exposition of boundary value problems for an extensive class of kinetic equations. These equations describe the transport of particles, momentum, energy, etc. They include the equations of neutron transport theory, radiative transfer, and rarefied gas dynamics, as well as a plethora of additional applications in various areas of physics, chemistry, biology and engineering. Many new results, developed since 1982, are covered in this monograph. The mathematical problems addressed within this monograph deal with existence and uniqueness of solutions of initial-boundary value problems, as well as questions of positivity, continuity, growth, stability, explicit representation of solutions, and equivalence of various formulations of the transport equations under consideration. The basic assumption underlying all kinetic equations studied in this monograph is that the particle flux of radiation does not interact with itself in a many-body sense, but only with the given host medium or with its own thermal equilibrium distribution in a perturbative way, and with the boundary under a linear reflection law. That is to say, only linear or linearized equations are treated. The monograph was intended to be self-contained, and specialized topics in analysis, as well as the physical background of examples, are outlined as they are introduced. The presentation comprises 13 chapters in 479 pages, followed by an extensive bibliography of 407 references.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 85A25
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 4013113
zbMATH Keywords: kinetic equations
zbMATH Keywords: transport of particles
zbMATH Keywords: neutron transport
zbMATH Keywords: radiative transfer
zbMATH Keywords: rarefied gas dynamics
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: initial-boundary value problems
zbMATH Keywords: positivity
zbMATH Keywords: continuity
zbMATH Keywords: growth
zbMATH Keywords: stability
zbMATH Keywords: explicit representation
zbMATH Keywords: bibliography
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4013113