Domain of Definition of Levermore's Five-Moment System
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The simplest system in Levermore's moment hierarchy involving moments higher than second order is the five-moment closure. It is obtained by taking velocity moments of the one-dimensional Boltzmann equation under the assumption that the velocity distribution is a maximum-entropy function. The moment vectors for which a maximum-entropy function exists consequently make up the domain of definition of the system. The aim of this article is a complete characterization of the structure of the domain of definition and the connected maximum-entropy problem. The space-homogeneous case of the equation and numerical aspects are also addressed.
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- 1.N. I. Akhiezer and M. Krein, Some Questions in the Theory of Moments, Transl. of Math. Monographs, Vol. 2, 1962.Google Scholar
- 2.N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis (Oliver & Boyd, 1965).Google Scholar
- 3.W. Dreyer, Maximisation of the entropy in non-equilibrium, J. Phys. A: Math. Gen. 20:6505–6517 (1987).Google Scholar
- 4.A. Kociszewski, The existence conditions for maximum entropy distributions, having prescribed the first three moments, J. Phys. A: Math. Gen. 19:L823–L827 (1986).Google Scholar
- 5.P. Le Tallec and J. P. Perlat, Numerical analysis of Levermore's moment system, Rapport de recherche No. 3124, INRIA Rocquencourt, 1997.Google Scholar
- 6.C. D. Levermore, Moment closure hierarchies for kinetic theories, J. Stat. Phys. 83:1021–1065 (1996).Google Scholar
- 7.A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (Springer, 1984).Google Scholar
- 8.L. R. Mead and N. Papanicolaou, Maximum entropy in the problem of moments, J. Math. Phys. 25:2404–2417 (1984).Google Scholar
- 9.I. Müller and T. Ruggeri, Extended Thermodynamics (Springer Verlag, New York, 1993).Google Scholar
- 10.S. Ihara, Information Theory for Continuous Systems (World Scientific, 1993).Google Scholar