Maximum entropy approach to the collisional Vlasov equation: Exact solutions

J.-H. Schönfeldt and A.R. Plastino

Physica A: Statistical Mechanics and its Applications, 2006, vol. 369, issue 2, 408-416

Abstract: We show that the maximum entropy approach proposed by El-Wakil, Elhanbaly, and Abdou (from now on EEA) in [S.A. El-Wakil, A. Elhanbaly, M.A. Abdou, Physica A 323 (2003) 213] for solving approximately the collisional Vlasov equation actually can provide exact solutions if properly implemented. We consider here two alternative procedures for obtaining exact maximum entropy solutions of the aforementioned equation. On the one hand, after identifying an appropriate set of relevant mean values (moments), we show that there are exact maximum entropy solutions associated with that set of moments. These solutions can be studied focusing either on the equations of motion of the moments themselves, or on the equations of motion of the corresponding Lagrange multipliers. On the other hand, it is possible to find exact solutions of the reduced equation considered by EEA, if one takes explicitly into account the zeroth-order moment of the solutions.

Keywords: Maximum entropy; Vlasov equation (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:369:y:2006:i:2:p:408-416

DOI: 10.1016/j.physa.2006.02.002

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