2026-04-03T20:10:05Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4524092024-06-06T09:43:28Zcom_2072_98col_2072_378195

00925njm 22002777a 4500 dc Carrillo de la Plata, José Antonio author Toscani, Giuseppe author Centre de Recerca Matemàtica, 730 author 2007 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. Probabilitats, Mesures de Equacions diferencials parcials Maxwell-boltzmann, Llei de distribució de Contractive probability metrics and asymptotic behavior of dissipative kinetic equations