On the linearized relativistic Boltzmann equation. I: Existence of solutions
type: Item
instance of: scholarly article
title: On the linearized relativistic Boltzmann equation. I: Existence of solutions
zbMATH Open document ID: 0653.76052
DOI: 10.1007/BF01224130
author: Marek Dudyński
author: Maria L. Ekiel-Jeżewska
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: The topic of this paper is the linearized relativistic Boltzmann equation in L 2(r,p) (r is a position variable, p a velocity variable). For a wide class of scattering cross sections, the collision operator L is shown to be representable as \(L=-\nu (p)+K\), where \(\nu\) (p) is a multiplication operator and K is compact. The dependence of \(\nu\) (p) on the scattering cross section is investigated in detail, and an existence and uniqueness theorem is proved.
reviewed by: Reinhard Illner
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 76Y05
Mathematics Subject Classification ID: 82B40
zbMATH DE Number: 4066542
zbMATH Keywords: linearized relativistic Boltzmann equation
zbMATH Keywords: scattering cross sections
zbMATH Keywords: collision operator
zbMATH Keywords: multiplication operator
zbMATH Keywords: scattering
zbMATH Keywords: uniqueness theorem
MaRDI profile type: Publication
cites work: Q5683176
cites work: Existence, uniqueness, and local stability for the Einstein-Maxwell- Boltzmann system
cites work: Asymptotic Theory of the Boltzmann Equation
cites work: Q5521434
cites work: The first and second fluid approximation to the linearized Boltzmann equation
cites work: The projection of the Navier-Stokes equations upon the Euler equations
cites work: Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
cites work: On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
cites work: The Linearized Boltzmann Collision Operator for Cut-Off Potentials
cites work: Q5585271
cites work: Q4188958
cites work: Mathematical aspects of relativistic kinetic theory
cites work: Applications of functional analysis and operator theory
cites work: The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
cites work: On the essential spectrum of an arbitrary operator. I
cites work: On the existence of global solutions of mixed problem for non-linear Boltzmann equation
cites work: Global solutions to the initial value problem for the nonlinear Boltzmann equation
cites work: Q4073917
cites work: Q4724364
cites work: Q3085749
description: scientific article; zbMATH DE number 4066542