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Théorèmes asymptotiques pour les équations de Boltzmann et de Landau

Abstract : This thesis is concerned with kinetic theory and many-particle systems in the setting of Boltzmann and Landau equations. Firstly, we study the derivation of kinetic equation as mean field limits of many-particle systems, using the concept of propagation of chaos. More precisely, we study chaotic probabilities on the phase space of such particle systems : the Boltzmann's sphere, which corresponds to the phase space of a many-particle system undergoing a dynamics that conserves momentum and energy ; and the Kac's sphere, which corresponds to the energy conservation only. Then we are concerned with the propagation of chaos, with quantitative and uniform in time estimates, for Boltzmann and Landau equations. Secondly, we study the long-time behaviour of solutions to the Landau equation.
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Kléber Carrapatoso Nascimento Junior Carrapatoso. Théorèmes asymptotiques pour les équations de Boltzmann et de Landau. Mathématiques générales [math.GM]. Université Paris Dauphine - Paris IX, 2013. Français. ⟨NNT : 2013PA090047⟩. ⟨tel-00920455v2⟩

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