Free access
Issue
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
Page(s) 443 - 463
DOI http://dx.doi.org/10.1051/m2an/2011051
Published online 24 October 2011
  1. L. Arlotti and M. Lachowicz, Euler and Navier-Stokes limits of the Uehling-Uhlenbeck quantum kinetic equations. J. Math. Phys. 38 (1997) 3571–3588. [CrossRef] [MathSciNet]
  2. T. Carleman, Sur la théorie de l’équation intégrodifférentielle de Boltzmann. Acta Math. 60 (1933) 91–146. [CrossRef] [MathSciNet]
  3. C. Cercignani, The Boltzmann Equation and Its Applications. Springer-Verlag, New York (1988).
  4. G. Dimarco and L. Pareschi, Exponential Runge-Kutta methods for stiff kinetic equations. arXiv:1010.1472.
  5. M. Escobedo and S. Mischler, On a quantum Boltzmann equation for a gas of photons. J. Math. Pures Appl. 80 (2001) 471–515. [CrossRef] [MathSciNet]
  6. F. Filbet and S. Jin, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources. J. Comput. Phys. 229 (2010) 7625–7648. [CrossRef] [MathSciNet]
  7. F. Filbet, C. Mouhot and L. Pareschi, Solving the Boltzmann equation in NlogN. SIAM J. Sci. Comput. 28 (2006) 1029–1053. [CrossRef] [MathSciNet]
  8. T. Goudon, S. Jin, J.-G. Liu and B. Yan, Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows. Preprint.
  9. J.W. Hu and S. Jin, On kinetic flux vector splitting schemes for quantum Euler equations. KRM 4 (2011) 517–530. [CrossRef]
  10. J.W. Hu and L. Ying, A fast spectral algorithm for the quantum Boltzmann collision operator. Preprint.
  11. R.J. LeVeque, Numerical Methods for Conservation Laws, 2nd edition. Birkhäuser Verlag, Basel (1992).
  12. X. Lu, A modified Boltzmann equation for Bose-Einstein particles: isotropic solutions and long-time behavior. J. Statist. Phys. 98 (2000) 1335–1394. [CrossRef] [MathSciNet]
  13. X. Lu, On spatially homogeneous solutions of a modified Boltzmann equation for Fermi-Dirac particles. J. Statist. Phys. 105 (2001) 353–388. [CrossRef] [MathSciNet]
  14. X. Lu and B. Wennberg, On stability and strong convergence for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Arch. Ration. Mech. Anal. 168 (2003) 1–34. [CrossRef] [MathSciNet]
  15. P. Markowich and L. Pareschi, Fast, conservative and entropic numerical methods for the Bosonic Boltzmann equation. Numer. Math. 99 (2005) 509–532. [CrossRef] [MathSciNet]
  16. C. Mouhot and L. Pareschi, Fast algorithms for computing the Boltzmann collision operator. Math. Comput. 75 (2006) 1833–1852. [CrossRef]
  17. L.W. Nordheim, On the kinetic method in the new statistics and its application in the electron theory of conductivity. Proc. R. Soc. Lond. Ser. A 119 (1928) 689–698. [CrossRef]
  18. L. Pareschi and G. Russo, Numerical solution of the Boltzmann equation I. Spectrally accurate approximation of the collision operator. SIAM J. Numer. Anal. 37 (2000) 1217–1245. [CrossRef] [MathSciNet]
  19. L. Pareschi and G. Russo, Implicit-Explicit Runge-Kutta methods and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25 (2005) 129–155. [CrossRef] [MathSciNet]
  20. W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3th edition. Cambridge University Press, Cambridge (2007).
  21. E.A. Uehling and G.E. Uhlenbeck, Transport phenomena in Einstein-Bose and Fermi-Dirac gases. I. Phys. Rev. 43 (1933) 552–561. [CrossRef]
  22. C. Villani, A review of mathematical topics in collisional kinetic theory, in Handbook of Mathematical Fluid Mechanics I. edited by S. Friedlander and D. Serre, North-Holland (2002) 71–305.

Recommended for you