Quantum Boltzmann Equations and Bose Einstein Condensation



We are interested in the mathematical theory for Quantum Boltzmann type equations such as local and global existence of solutions, singularity formation, particular solutions.

Some publications:

  1. A Nonlinear Fokker-Planck equation modelling the approach to thermal equilibrium in a homogeneous plasma
     Trans. of the A.M.S. Vol. 350 (1998); pp. 3837-3901.
    Miguel Escobedo, Miguel A. Herrero and Juan J. L. Velazquez

  2. Radiation in a homogeneous plasma.
     Physica D Vol. 126 (1999); pp. 236-260.
    Miguel Escobedo, Miguel A. Herrero and Juan J. L. Velazquez

  3. Homogeneous Boltzmann equation in quantum relativistic kinetic theory
     Electronic J. Diff. Eqns., Monograph 04 (2003).
    Miguel Escobedo, Stéphane Mischler and Manuel A. Valle

  4. On a quantum Boltzmann equation for a gas of photons
     J. Math. Pures Appl. Vol. 80 (2001); pp. 471-515.
    Miguel Escobedo and Stéphane Mischler.

  5. Asymptotic description of Dirac mass formation in kinetic equations for quantum particles
     J. Diff. Eqns. Vol. 202 (2004); pp. 208-230.
    Miguel Escobedo, Stéphane Mischler and Juan J. L. Velazquez.

  6. Maximization entropy problem for quantum relativistic particles
     Bull. S.M.F. Vol. 133 (2005); pp. 87-120.
    Miguel Escobedo, Stéphane Mischler and Manuel A. Valle.