Generalized solutions of the radiative transfer equations in a singular case
type: Item
instance of: scholarly article
title: Generalized solutions of the radiative transfer equations in a singular case
zbMATH Open document ID: 0614.35084
DOI: 10.1007/BF01454973
author: François Golse
author: Ben{ôı}t Perthame
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: This paper deals with a pair of nonlinear PDEs which may be regarded as a perturbation of the well-known transport equation. These equations are classical in astrophysics and represent the evolution of a stellar atmosphere in the absence of hydrodynamic motion and heat conduction. The local thermodynamic equilibrium is assumed for the matter. The purpose of this paper is to study the Cauchy problem. The main text of this paper is organized as follows. The assumptions and main results are stated in Section I, where some heuristic derivations for the theorems are also given. Section II was devoted to the existence proof and the maximum principle. This proof relies mainly on a nonlinear version of Hille-Yosida theorem. In Section III, the generalized solution of the radiative transfer equations is proved to be classical when the initial energy is uniformly positive. The uniqueness of the semigroup solving these equations is deduced from this proof. A bounded variation regularity theorem of the generalized solutions in the degenerate case is proved in Section IV, when the temperature is allowed to vanish. Finally the convergence of some splitting algorithms associated to the radiative transfer equations was proved in Section V.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 85A20
Mathematics Subject Classification ID: 85A25
zbMATH DE Number: 3994156
zbMATH Keywords: perturbation
zbMATH Keywords: transport equation
zbMATH Keywords: evolution of a stellar atmosphere
zbMATH Keywords: local thermodynamic equilibrium
zbMATH Keywords: Cauchy problem
zbMATH Keywords: existence
zbMATH Keywords: maximum principle
zbMATH Keywords: generalized solution
zbMATH Keywords: radiative transfer
zbMATH Keywords: semigroup
zbMATH Keywords: bounded variation regularity
MaRDI profile type: Publication
Wikidata QID: Q60503006
cites work: Q4094029
cites work: Convergence and approximation of semigroups of nonlinear operators in Banach spaces
cites work: Q3684649
cites work: Q3793191
cites work: Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
cites work: Q3924584
cites work: Q3688976
cites work: Splitting Algorithms for the Sum of Two Nonlinear Operators
cites work: Application of Accretive Operators Theory to the Radiative Transfer Equations
full work available at URL: https://doi.org/10.1007/bf01454973
OpenAlex ID: W2027193336
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description: scientific article; zbMATH DE number 3994156