Strong convergence towards homogeneous cooling states for dissipative Maxwell models

Eric A. Carlen, José A. Carrillo, Maria C. Carvalho

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12 Citations (Scopus)

Abstract

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogeneous cooling state present in the literature implies the strong convergence in Sobolev norms and in the L1 norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the L1 distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero. © 2008 Elsevier Masson SAS. All rights reserved.
Original languageEnglish
Pages (from-to)1675-1700
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume26
Issue number5
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Dissipative Maxwell models
  • Long time asymptotics
  • Propagation of regularity
  • Self-similarity
  • Small inelasticity limit
  • Strong convergence

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