Electronic Journal of Differential Equations,
Monograph 04, 2003. (85 pages)
Title: Homogeneous Boltzmann equation in quantum relativistic kinetic theory
Authors: Miguel Escobedo (Univ. del Pais Vasco, Spain)
Stephane Mischler (Ecole Normale Super., France)
Manuel A. Valle (Univ. del Pais Vasco, Spain)
Abstract:
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.