## On the approximation of kinetic equations by moment systems

• The aim of this article is to show that moment approximations of kinetic equations based on a Maximum Entropy approach can suffer from severe drawbacks if the kinetic velocity space is unbounded. As example, we study the Fokker Planck equation where explicit expressions for the moments of solutions to Riemann problems can be derived. The quality of the closure relation obtained from the Maximum Entropy approach as well as the Hermite/Grad approach is studied in the case of five moments. It turns out that the Maximum Entropy closure is even singular in equilibrium states while the Hermite/Grad closure behaves reasonably. In particular, the admissible moments may lead to arbitrary large speeds of propagation, even for initial data arbitrary close to global eqilibrium.

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Verfasserangaben: Wolfgang Dreyer, Michael Junk, Matthias Kunik urn:nbn:de:hbz:386-kluedo-10516 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (229) Preprint Englisch 2000 2000 Technische Universität Kaiserslautern 17.08.2000 Fokker-Planck equation ; Grad expansion ; exact solution ; maximum entropy ; moment methods ; moment realizability Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C70 Transport processes Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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