Self similar solutions in one-dimensional kinetic models: a probabilistic view (Articolo in rivista)

Type
Label
  • Self similar solutions in one-dimensional kinetic models: a probabilistic view (Articolo in rivista) (literal)
Anno
  • 2010-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1214/11-AAP818 (literal)
Alternative label
  • Federico Bassetti; Lucia Ladelli (2010)
    Self similar solutions in one-dimensional kinetic models: a probabilistic view
    in The Annals of applied probability; Institute Of Mathematical Statistics, Cleveland (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Federico Bassetti; Lucia Ladelli (literal)
Pagina inizio
  • 1928 (literal)
Pagina fine
  • 1961 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 22 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 5 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Università degli Studi di Pavia; Politecnico di Milano (literal)
Titolo
  • Self similar solutions in one-dimensional kinetic models: a probabilistic view (literal)
Abstract
  • This paper deals with a class of Boltzmann equations on the real line, extensions of the well-known Kac caricature. A distinguishing feature of the corresponding equations is that the therein collision gain operators are defined by $N$-linear smoothing transformations. This kind of problems have been studied, from an essentially analytic viewpoint, in a recent paper by Bobylev, Gamba and Cercignani. Instead, the present work rests exclusively on probabilistic methods, based on techniques pertaining to the classical central limit problem and to the so-called fixed-point equations for probability distributions. An advantage of resorting to methods from the probability theory is that the same results - relative to self-similar solutions - as those obtained by Bobylev, Gamba and Cercignani, are here deduced under weaker conditions. In particular, it is shown how convergence to self--similar solution depends on the belonging of the initial datum to the domain of attraction of a specific stable distribution. Moreover, some results on the speed of convergence are given in terms of Kantorovich-Wasserstein and Zolotarev distances between probability measures. (literal)
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