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      Infinite energy solutions to the homogeneous Boltzmann equation

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          Abstract

          The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which 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 {\it 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. {\bf 106} (2002), 1039--1071].

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          Most cited references 11

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          The Boltzmann Equation

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            Some theorems on stable processes

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              On the spatially homogeneous Boltzmann equation

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                Author and article information

                Journal
                09 July 2009
                Article
                0907.1676

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                82C40; 76P05
                math.AP math-ph math.MP

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