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Discrete velocity models with general boundary conditions in a slab
Author(s) -
Cercignani Carlo,
Illner Reinhard
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(200102)24:3<137::aid-mma197>3.0.co;2-h
Subject(s) - mathematics , boundary (topology) , mathematical analysis , boundary value problem , slab , zero (linguistics) , component (thermodynamics) , point (geometry) , fixed point theorem , geometry , physics , linguistics , philosophy , geophysics , thermodynamics
We consider a gas between parallel plates, described by a discrete velocity model. At the boundary, we impose the most general linear boundary conditions which preserve mass. Using a fixed‐point theorem we prove the existence of at least one parameter family of solutions, continuous in x . The velocities are assumed to have a non‐zero component in the direction orthogonal to the boundaries. Copyright © 2001 John Wiley & Sons, Ltd.