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A completely solvable model of the nonlinear Boltzmann equation

Author

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  • Ruijgrok, Th.W.
  • Wu, Tai Tsun

Abstract

In one space and one time dimension, a model of the nonlinear Boltzmann equation is presented that is exactly solvable for all initial conditions. Furthermore, this model has the following desirable properties: (i) conservation of the number of particles; (ii) energy conservation; (iii) nonlinearity; (iv) positivity of distribution functions; and (v) unique equilibrium state (for any given density) which is approached as t → ∞ for most physically interesting initial conditions. Some of the simple properties of this model are studied.

Suggested Citation

  • Ruijgrok, Th.W. & Wu, Tai Tsun, 1982. "A completely solvable model of the nonlinear Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(3), pages 401-416.
    • Handle: RePEc:eee:phsmap:v:113:y:1982:i:3:p:401-416
    DOI: 10.1016/0378-4371(82)90147-9
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    Cited by:

    1. R. Filliger & M.-O. Hongler & L. Streit, 2008. "Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 497-505, June.

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