Completely solvable models of the nonlinear Boltzmann equation. I: Case of three velocities. (English) Zbl 0731.76066
The authors investigate a class of models of the nonlinear Boltzmann equation that are exactly solvable for all initial conditions. The models have three velocity components and the following properties: a) conservation of the number of particles, b) energy conservation, c) nonlinearity, d) positivity of distribution functions and e) unique equilibrium state. Three numerical examples showing the interaction between the three distributions are given.
Reviewer: I.Grosu (Iaşi)
MSC:
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
Keywords:
nonlinear Boltzmann equation; energy conservation; distribution functions; unique equilibrium stateReferences:
| [1] | DOI: 10.1103/PhysRevLett.36.1107 · doi:10.1103/PhysRevLett.36.1107 |
| [2] | Bobylev A. V., Sov. Phys. Dokl. 20 pp 820– (1976) |
| [3] | DOI: 10.1103/PhysRevA.25.3393 · doi:10.1103/PhysRevA.25.3393 |
| [4] | DOI: 10.1063/1.1705172 · Zbl 0155.32604 · doi:10.1063/1.1705172 |
| [5] | DOI: 10.1063/1.1705172 · Zbl 0155.32604 · doi:10.1063/1.1705172 |
| [6] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [7] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [8] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [9] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [10] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [11] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [12] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [13] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [14] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [15] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [16] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [17] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [18] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [19] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [20] | DOI: 10.1063/1.864558 · Zbl 0548.76060 · doi:10.1063/1.864558 |
| [21] | DOI: 10.1063/1.527514 · Zbl 0641.76070 · doi:10.1063/1.527514 |
| [22] | DOI: 10.1063/1.527514 · Zbl 0641.76070 · doi:10.1063/1.527514 |
| [23] | DOI: 10.1063/1.527514 · Zbl 0641.76070 · doi:10.1063/1.527514 |
| [24] | DOI: 10.1063/1.527514 · Zbl 0641.76070 · doi:10.1063/1.527514 |
| [25] | DOI: 10.1016/0378-4371(82)90147-9 · doi:10.1016/0378-4371(82)90147-9 |
| [26] | DOI: 10.1103/PhysRevLett.13.138 · doi:10.1103/PhysRevLett.13.138 |
| [27] | DOI: 10.1111/j.2164-0947.1980.tb03018.x · doi:10.1111/j.2164-0947.1980.tb03018.x |
| [28] | DOI: 10.1111/j.2164-0947.1980.tb03018.x · doi:10.1111/j.2164-0947.1980.tb03018.x |
| [29] | DOI: 10.1111/j.2164-0947.1980.tb03018.x · doi:10.1111/j.2164-0947.1980.tb03018.x |
| [30] | DOI: 10.1111/j.2164-0947.1980.tb03018.x · doi:10.1111/j.2164-0947.1980.tb03018.x |
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