Journal of the Mathematical Society of Japan

Solutions to the discrete Boltzmann equation with general boundary conditions

Yoshiko NIKKUNI and Reiko SAKAMOTO

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 3 (1999), 757-779.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107915

Digital Object Identifier
doi:10.2969/jmsj/05130757

Mathematical Reviews number (MathSciNet)
MR1691453

Zentralblatt MATH identifier
0939.35156

Subjects
Primary: 35Q99: None of the above, but in this section
Secondary: 76P05: Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 82C40: Kinetic theory of gases

Keywords
Discrete Boltzmann equation boundary condition time-global solution stationary solution eigenvalue

Citation

NIKKUNI, Yoshiko; SAKAMOTO, Reiko. Solutions to the discrete Boltzmann equation with general boundary conditions. J. Math. Soc. Japan 51 (1999), no. 3, 757--779. doi:10.2969/jmsj/05130757. https://projecteuclid.org/euclid.jmsj/1213107915


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