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.