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Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior

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Date
2006
Link to item file
http://hal.archives-ouvertes.fr/hal-00087235/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
tail behavior; regularity of the collision operator; self-similar solutions; Haff's law; cooling process; granular gas; inelastic hard spheres; Boltzmann equation
Journal issue
Journal of Statistical Physics
Volume
124
Number
2-4
Publication date
2006
Article pages
703-746
DOI
http://dx.doi.org/10.1007/s10955-006-9097-8
URI
https://basepub.dauphine.fr/handle/123456789/943
Collections
  • CEREMADE : Publications
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Author
Mouhot, Clément
Mischler, Stéphane
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff 's law on the rate of decay of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases.

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