Geodesic
Why do Solutions of the Maxwell-Boltzmann Equation Tend to be Gaussians? A Simple Answer
Documenta mathematica, Tome 22 (2017), pp. 1267-1273.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The Maxwell-Boltzmann functional equation has recently attraction renewed interest since besides its importance in Boltzmann's kinetic theory of gases it also characterizes maximizers of certain bilinear estimates for solutions of the free Schrödinger equation. In this note we give a short and simple proof that, under some mild growth restrictions, any measurable complex-valued solution of the Maxwell-Boltzmann equation is a Gaussian. This covers most, if not all, of the applications.
Classification : 39B32, 82C40
Keywords: Maxwell-Boltzmann functional equation, Gaussian maximizers, kinetic theory of gases, Schrödinger equation, measurable complex-valued solution 
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Hundertmark, Dirk; Lee, Young-Ran. Why do Solutions of the Maxwell-Boltzmann Equation Tend to be Gaussians? A Simple Answer. Documenta mathematica, Tome 22 (2017), pp. 1267-1273. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a15/