Open Access
July, 1999 Solutions to the discrete Boltzmann equation with general boundary conditions
J. Math. Soc. Japan 51(3): 757-779 (July, 1999). DOI: 10.2969/jmsj/05130757


We study the initial-boundary value problems and the corresponding stationary problems of the one-dimensional discrete Boltzmann equation in a bounded region. The boundary conditions considered are of mixed type and involve both the reflection and diffusion parts. It is shown that a unique solution to the initial-boundary value problem exists globally in time under the general situation that the reflection parts of both the boundary conditions do not increase the number of gas particles. Furthermore, it is proved that stationary solutions exist under the restriction that the reflection part of the boundary condition on one side really decreases the number of gas particles. This restriction plays an essential role in proving the existence result.


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Yoshiko NIKKUNI. Reiko SAKAMOTO. "Solutions to the discrete Boltzmann equation with general boundary conditions." J. Math. Soc. Japan 51 (3) 757 - 779, July, 1999.


Published: July, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0939.35156
MathSciNet: MR1691453
Digital Object Identifier: 10.2969/jmsj/05130757

Primary: 35Q99
Secondary: 76P05 , 82C40

Keywords: boundary condition , discrete Boltzmann equation , eigenvalue , stationary solution , time-global solution

Rights: Copyright © 1999 Mathematical Society of Japan

Vol.51 • No. 3 • July, 1999
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