Free Access
Issue
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
Page(s) 443 - 463
DOI https://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] [Google Scholar]
  2. T. Carleman, Sur la théorie de l’équation intégrodifférentielle de Boltzmann. Acta Math. 60 (1933) 91–146. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Cercignani, The Boltzmann Equation and Its Applications. Springer-Verlag, New York (1988). [Google Scholar]
  4. G. Dimarco and L. Pareschi, Exponential Runge-Kutta methods for stiff kinetic equations. arXiv:1010.1472. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  7. F. Filbet, C. Mouhot and L. Pareschi, Solving the Boltzmann equation in NlogN. SIAM J. Sci. Comput. 28 (2006) 1029–1053. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Goudon, S. Jin, J.-G. Liu and B. Yan, Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows. Preprint. [Google Scholar]
  9. J.W. Hu and S. Jin, On kinetic flux vector splitting schemes for quantum Euler equations. KRM 4 (2011) 517–530. [CrossRef] [Google Scholar]
  10. J.W. Hu and L. Ying, A fast spectral algorithm for the quantum Boltzmann collision operator. Preprint. [Google Scholar]
  11. R.J. LeVeque, Numerical Methods for Conservation Laws, 2nd edition. Birkhäuser Verlag, Basel (1992). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  16. C. Mouhot and L. Pareschi, Fast algorithms for computing the Boltzmann collision operator. Math. Comput. 75 (2006) 1833–1852. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you