Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Toscani, Giuseppe (Università di Pavia. Dipartimento di Matematica)
Centre de Recerca Matemàtica, 730

Imprint:	Centre de Recerca Matemàtica 2007
Description:	116 p.
Abstract:	The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Series:	Centre de Recerca Matemàtica. Prepublicacions
Series:	Prepublicacions del Centre de Recerca Matemàtica ; 730
Document:	Article ; Prepublicació ; Versió de l'autor
Subject:	Probabilitats, Mesures de ; Equacions diferencials parcials ; Maxwell-boltzmann, Llei de distribució de

116 p, 619.5 KB

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