Electron. J. Diff. Eqns., Monograph 04 (2003), 85 pages.

Homogeneous Boltzmann equation in quantum relativistic kinetic theory

Miguel Escobedo, Stephane Mischler, & Manuel A. Valle

We consider some mathematical questions about Boltzmann equations for quantum particles, relativistic or non relativistic. Relevant particular cases such as Bose, Bose-Fermi, and photon-electron gases are studied. We also consider some simplifications such as the isotropy of the distribution functions and the asymptotic limits (systems where one of the species is at equilibrium). This gives rise to interesting mathematical questions from a physical point of view. New results are presented about the existence and long time behaviour of the solutions to some of these problems.

Submitted November 29, 2002. Published January 20, 2003.
Math Subject Classifications: 82B40, 82C40, 83-02.
Key Words: Boltzmann equation, relativistic particles, entropy maximization, Bose distribution, Fermi distribution, Compton scattering, Kompaneets equation.
DOI: https://doi.org/10.58997/ejde.mon.04

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Miguel Escobedo
Departamento de Matematicas,
Universidad del Pais Vasco
Apartado 644 Bilbao E 48080, Spain
e-mail: mtpesmam@lg.ehu.es
Stephane Mischler
DMA, Ecole Normale Superieure
Paris Cedex 05 F 75230, France
e-mail: Mischler@math.uvsq.fr
Manuel A. Valle
Departamento de Fisica Teorica e Historia de la Ciencia
Universidad del Pais Vasco
Apartado 644 Bilbao E48080, Spain
email: wtpvabam@lg.ehu.es

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