Published in

Springer Verlag, Ima Volumes in Mathematics and Its Applications, p. 37-56, 2004

DOI: 10.1007/978-1-4613-0017-5_2

Links

Tools

Export citation

Search in Google Scholar

Steady States for Streater’s Energy-Transport Models of Self-Gravitating Particles

Journal article published in 2004 by Piotr Biler, Jean Dolbeault ORCID, Maria J. Esteban, Peter A. Markowich, Instytut Matematyczny, Tadeusz Nadzieja, Instytut Matematyki
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Upload
Green circle
Postprint: archiving allowed
Upload
Red circle
Published version: archiving forbidden
Policy details
Data provided by SHERPA/RoMEO

Abstract

We review Streater's energy-transport models which describe the temporal evolution of the density and temperature of a cloud of gravitating particles, coupled to a mean field Poisson equation. In particular we consider the existence of stationary solutions in a bounded domain with given energy and mass. We discuss the influence of the dimension and geometry of the domain on existence results. Key words and phrases: Streater's models, drift-diffusion systems, energy, existence and uniqueness of stationary solutions, Poisson--Boltzmann--Emden equation. 2000 Mathematics Subject Classification: 35Q, 35J60, 82C 1 1 Introduction Recently, R. F. Streater derived systems of partial differential equations that describe the dynamics of Brownian particles in the presence of an external potential as well as the accompanying thermodynamic processes, cf. [37, 38, 39] (and [40] for further extensions), as generalizations of the classical Smoluchowski equation (cf. [36]). The paper [6] gave an ex...