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Homogeneous Boltzmann equation in quantum relativistic kinetic theory

Author(s): Miguel Escobedo | Stephane Mischler | Manuel A. Valle

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: Monographs;
Issue: 04;
Start page: 1;
Date: 2003;
Original page

Keywords: Boltzmann equation | relativistic particles | entropy maximization | Bose distribution | Fermi distribution | Compton scattering | Kompaneets equation.

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.

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