Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 11
100
Views
0
CrossRef citations to date
0
Altmetric
Articles

The existence and convergence of the Maxwell model for granular materials

&
Pages 2383-2396 | Received 16 Apr 2012, Accepted 02 Sep 2015, Published online: 14 Oct 2015

References

  • Bobylev AV, Carrillo JA, Gamba I. On some properties of kinetic and hydrodynamics equations for inelastic interactions. J. Stat. Phys. 2000;98:743–773.
  • Bobylev AV, Cercignani C. Moment equations for granular material in a thermal bath. J. Stat. Phys. 2002;106:547–567.
  • Cercignani C, Iiiner R, Stocia C. On diffusive equilibria in generalized kinetic theory. J. Stat. Phys. 2001;105:337–352.
  • Bisi M, Carrillo JA, Toscani G. Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibria. J. Stat. Phys. 2005;118:301–331.
  • Alonso RJ. Existence of global solutions to the Cauchy problem for the inelastic Boltzmann equation with near-vacuum data. Indiana Univ. Math. J. 2009;58:999–1022.
  • Bellomo N, Pulvirenti M. On the one-dimensional Boltzmann equation for granular flow. Math. Model. Numer. Anal. 2003;35:899–905.
  • Bobylev AV, Cercignani C. Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. J. Stat. Phys. 2003;110:333–375.
  • Carrillo JA, Cercignani C, Gamba I. Steady state of a Boltzmann equation for driven media. Phys. Rev. E. 2000;62:7700–7707.
  • Ernst MH, Brito R. High energy tails or inelastic Maxwell models. Europhys. Lett. 2002;58:183–187.
  • Gamba I, Panferov V, Villani C. On the Boltzmann equations for diffusively excited granular media. Commun. Math. Phys. 2004;246:503–541.
  • Li H, Toscani G. Long-time asymptotics of kinetic models of granular flows. Arch. Ration. Mech. Anal. 2004;172:407–428.
  • Mischler S, Mouhot C. Cooling process for inelastic Boltzmann equation for hard spheres. Part I: the problem and tail behavior. J. Stat. Phys. 2006;124:605–702.
  • Mischler S, Mouhot C. Cooling process for inelastic Boltzmann equation for hard spheres. Part II: self-similar solution and tail behavior. J. Stat. Phys. 2006;124:703–746.
  • Mischler S, Mouhot C. Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres. Commun. Math. Phys. 2009;288:431–502.
  • Villani C. Mathematics of granular material. J. Stat. Phys. 2006;124:655–702.
  • Wei J, Zhang X. On the Cauchy problem for the inelastic Boltzmann equation with external force. J. Stat. Phys. 2012;146:592–609.
  • Carlen E, Gabetta G, Toscani G. Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas. Commun. Math. Phys. 1999;199:521–546.
  • Gabetta G, Toscani G, Wennberg B. Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation. J. Stat. Phys. 1995;81:901–934.
  • Toscani G, Villani C. Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. J. Stat. Phys. 1999;94:619–637.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.