Group Analysis of the One-Dimensional Boltzmann Equation: III. Condition for the Moment Quantities to Be Physically Meaningful
| Autor: | K. S. Platonova, Aleksey Vladislavovich Borovskikh |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
010102 general mathematics Statistical and Nonlinear Physics Maximum dimension Symmetry group 01 natural sciences Boltzmann equation Force field (chemistry) Equivalence group Group analysis 0103 physical sciences 010307 mathematical physics 0101 mathematics Mathematical Physics Mathematical physics |
| Zdroj: | Theoretical and Mathematical Physics. 195:886-915 |
| ISSN: | 1573-9333 0040-5779 |
| DOI: | 10.1134/s0040577918060077 |
| Popis: | We present the group classification of the one-dimensional Boltzmann equation with respect to the function F = F(t, x, c) characterizing an external force field under the assumption that the physically meaningful constraints dx = c dt, dc = F dt, dt = 0, and dx =0 are imposed on the variables. We show that for all functions F, the algebra is finite-dimensional, and its maximum dimension is eight, which corresponds to the equation with a zero F. |
| Databáze: | OpenAIRE |
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