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Boundary Conditions and Existence Results for Levermore's Moments System

Perlat, Jean-Pierre; Le Tallec, Patrick (2000), Boundary Conditions and Existence Results for Levermore's Moments System, Mathematical Models and Methods in Applied Sciences, 10, 1, p. 127-152. http://dx.doi.org/10.1142/S0218202500000094

Type
Article accepté pour publication ou publié
Date
2000
Journal name
Mathematical Models and Methods in Applied Sciences
Volume
10
Number
1
Publisher
World Scientific
Pages
127-152
Publication identifier
Metadata
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Author(s)
Perlat, Jean-Pierre
Le Tallec, Patrick cc
Abstract (EN)
This paper considers the 14 moment expansion of the Boltzmann equation proposed by D. Levermore. After a brief review of this model, we derive weak boundary conditions compatible with the hyperbolic structure of the model, and express in average the microscopic boundary conditions imposed to the gas. This choice of half flux boundary conditions is justified by a mathematical analysis of the resulting linearized problem. Using standard parabolic regularization arguments and a specific dissipation inequality, we prove that the linearized problem has a unique solution.
Subjects / Keywords
Boltzmann equation; boundary conditions; linearized problem