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Infinite Energy Solutions to the Homogeneous Boltzmann Equation

Abstract : The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel that allows us to construct unique solutions to the initial value problem in a space of probability measures defined via the Fourier transform. In that space, the second moment of a measure is not assumed to be finite, so infinite energy solutions are not a priori excluded from our considerations. Moreover, we study the large-time asymptotics of solutions and, in a particular case, we give an elementary proof of the asymptotic stability of self-similar solutions obtained by A. V. Bobylev and C. Cercignani [J. Stat. Phys. 106 (2002), 1039-1071]. (C) 2009 Wiley Periodicals, Inc.
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  • HAL Id : hal-00693021, version 1


Marco Cannone, Grzegorz Karch. Infinite Energy Solutions to the Homogeneous Boltzmann Equation. Communications on Pure and Applied Mathematics, Wiley, 2010, 63 (6), pp.747--778. ⟨hal-00693021⟩



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