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Publication details

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 - Centro de Matemática e Aplicações Fundamentais 

Scope
International

Refereeing
Yes

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.

Date of Publication
2009-09

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

Publication Identifiers
ISSN - 0294-1449

Publisher
Elsevier BV

Volume
26
Number
5

Number of pages
25
Starting page
1675
Last page
1700

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


Export

APA
Eric A. Carlen, José A. Carrillo, Maria C. Carvalho, (2009). Strong convergence towards homogeneous cooling states for dissipative Maxwell models. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 26, 1675-1700. ISSN 0294-1449. eISSN . http://dx.doi.org/10.1016/j.anihpc.2008.10.005

IEEE
Eric A. Carlen, José A. Carrillo, Maria C. Carvalho, "Strong convergence towards homogeneous cooling states for dissipative Maxwell models" in Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol. 26, pp. 1675-1700, 2009. 10.1016/j.anihpc.2008.10.005

BIBTEX
@article{44956, author = {Eric A. Carlen and José A. Carrillo and Maria C. Carvalho}, title = {Strong convergence towards homogeneous cooling states for dissipative Maxwell models}, journal = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis}, year = 2009, pages = {1675-1700}, volume = 26 }