BIBLIOS

Document type
Journal articles

Document subtype
Full paper

Title
Strong convergence towards homogeneous cooling states for dissipative Maxwell models

Participants in the publication
Eric A. Carlen (Author)
RUTGERS UNIVERSITY
José A. Carrillo (Author)
UNIVERSITAT AUTONOMA DE BARCELONA
Maria C. Carvalho (Author)
Dep. Matemática
CMAF

Summary
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 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 distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.


Where published
Annales de l'Institut Henri Poincare (C) Non Linear Analysis

Publication Identifiers
ISSN - 0294-1449

Publisher
Elsevier BV



Document Identifiers
URL - http://dx.doi.org/10.1016/j.anihpc.2008.10.005
DOI - https://doi.org/10.1016/j.anihpc.2008.10.005

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