Time-Dependent Rescalings and Dispersion for the Boltzmann Equation
Dolbeault, Jean (1999), Time-Dependent Rescalings and Dispersion for the Boltzmann Equation. https://basepub.dauphine.fr/handle/123456789/6279
TypeDocument de travail / Working paper
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Abstract (EN)Using the notion of time-dependent rescalings introduced in [DR], we prove explicit dispersion results. The main tool is a Lyapunov functional which is given by the energy after rescaling and the entropy dissipation. The relation with asymptotically self-similar solutions is investigated. The method applies to the solutions of the Boltzmann, Landau and BGK equations. In the case of the Vlasov-Fokker-Planck equation, the diﬀerence with the self-similar solutions has a faster decay, which is estimated by a classical method for parabolic equations and interpolation estimates.
Subjects / KeywordsVlasov-Fokker-Planck equation; BGK equation; Landau equation; Boltzmann equation; entropy; Lyapunov functional; dispersion; time-dependent rescaling
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