A completely solvable model of the nonlinear Boltzmann equation |
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Authors: | ThW Ruijgrok Tai Tsun Wu |
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Institution: | Institute for Theoretical Physics, University of Utrecht, Utrecht, The Netherlands;Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany;Gordon McKay Laboratory, Harvard University, Cambridge, Mass., USA |
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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. |
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