Mathematical aspects of kinetic model equations for binary gas mixtures
| Autor: | David E. Greene |
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| Rok vydání: | 1975 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics. 16:776-782 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.522631 |
| Popis: | A system of integrodifferential equations, which has a structure similar to the Boltzmann equations for a binary gas mixture and which qualitatively describes wave propagation, is investigated. The Oppenheim model is used and a linear initial−value problem is considered. The initial−value problem is shown to be well set mathematically with certain specifications on the initial distribution functions. Justification is made for the use of Fourier−Laplace transforms. A discussion is made of the dispersion relation and its analytic continuation. The roots σ (k) of the dispersion relation are shown to lie in three distinct regions of the σ plane: the hydrodynamic region, the semihydrodynamic region, and the rarefied region. It is established that the roots σ (k) are bounded by −1 + δ < Reσ ⩽ 0 under the assumption of plane−wave solutions which implies that the system is stable and that plane waves cease to exist if Reσ ⩽ −1 + δ. |
| Databáze: | OpenAIRE |
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