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On the approximation of the Fokker-Planck equation by moment systems

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2001

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Dreyer, Wolfgang
Kunik, Matthias

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http://nbn-resolving.de/urn:nbn:de:bsz:352-254291
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https://doi.org/10.1088/0951-7715/14/4/314
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Nonlinearity. 2001, 14(4), pp. 881-906. ISSN 0951-7715. eISSN 1361-6544. Available under: doi: 10.1088/0951-7715/14/4/314

Zusammenfassung

The aim of this paper 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 arbitrarily large speeds of propagation, even for initial data arbitrary close to global eqilibrium.

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510 Mathematik

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ISO 690DREYER, Wolfgang, Michael JUNK, Matthias KUNIK, 2001. On the approximation of the Fokker-Planck equation by moment systems. In: Nonlinearity. 2001, 14(4), pp. 881-906. ISSN 0951-7715. eISSN 1361-6544. Available under: doi: 10.1088/0951-7715/14/4/314
BibTex
@article{Dreyer2001appro-25429,
  year={2001},
  doi={10.1088/0951-7715/14/4/314},
  title={On the approximation of the Fokker-Planck equation by moment systems},
  number={4},
  volume={14},
  issn={0951-7715},
  journal={Nonlinearity},
  pages={881--906},
  author={Dreyer, Wolfgang and Junk, Michael and Kunik, Matthias}
}
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