Proof of an Asymptotic Property of Self-Similar Solutions of the Boltzmann Equation for Granular Materials |
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Authors: | A V Bobylev C Cercignani G Toscani |
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Institution: | (1) Division of Engineering Sciences, Physics and Mathematics, Karlstad University, Karlstad, Sweden;(2) Dipartimento di Matematica, Politecnico di Milano, Milano, Italy |
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Abstract: | We consider a question related to the kinetic theory of granular materials. The model of hard spheres with inelastic collisions is replaced by a Maxwell model, characterized by a collision frequency independent of the relative speed of colliding particles. Our main result is that, in the space-homogeneous case, a self-similar asymptotics holds, as conjectured by Ernst–Brito. The proof holds for any initial distribution function with a finite moment of some order greater than two. |
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Keywords: | Granular material Boltzmann equation self-similar solutions |
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