On the Boltzmann equation for diffusively excited granular media

Details On the Boltzmann equation for diffusively excited granular media On the Boltzmann equation for diffusively excited granular media

2003-02-27

arxiv.org/abs/math/0302348v1

Mathematics

Analysis of PDEs

40 pages, 1 figure

Scientific paper

10.1007/s00220-004-1051-5

We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative $L^2$ function, with bounded mass and kinetic energy (second moment), we prove the existence of a solution to this model, which instantaneously becomes smooth and rapidly decaying. Under a weak additional assumption of bounded third moment, the solution is shown to be unique. We also establish the existence (but not uniqueness) of a stationary solution. In addition we show that the high-velocity tails of both the stationary and time-dependent particle distribution functions are overpopulated with respect to the Maxwellian distribution, as conjecturedby previous authors, and we prove pointwise lower estimates for the solutions.

Affiliated with

Also associated with

No associations

Rating

On the Boltzmann equation for diffusively excited granular media does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Boltzmann equation for diffusively excited granular media, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Boltzmann equation for diffusively excited granular media will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331071