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Global solutions of the Boltzmann equation on a lattice |
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| Authors: | Carlo Cercignani William Greenberg P F Zweifel |
| Institution: | (1) Istituto di Matematica del Politecnico di Milano, Milano, Italy;(2) Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia;(3) Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia |
| Abstract: | The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.Supported by National Science Foundation Grant ENG-7515882. |
| Keywords: | Boltzmann equation partial differential equations global solutions mild solutions lattice semigroup |
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