The nonlinear Boltzmann equation with partially absorbing boundary conditions. Global existence and uniqueness results

G. Toscani; V. Protopopescu

doi:10.1063/1.527560

The nonlinear Boltzmann equation with partially absorbing boundary conditions. Global existence and uniqueness results

G. Toscani, V. Protopopescu

Computational Sciences & Engineering Div

Research output: Contribution to journal › Article › peer-review

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Abstract

The method applied by Bellomo and Toscani [J. Math. Phys. 26, 334 ( 1985)] for the Boltzmann equation in an infinite medium to establish global results for bounded media with partially absorbing boundary conditions is generalized. The method does not require that the equilibrium solution be the vacuum state and, accordingly, does not rely on positivity/ monotonicity arguments. The growth produced by the nonlinearity is compensated by the combined effect of streaming and (partial) absorption (leakage) at the boundary.

Original language	English
Pages (from-to)	1140-1145
Number of pages	6
Journal	Journal of Mathematical Physics
Volume	28
Issue number	5
DOIs	https://doi.org/10.1063/1.527560
State	Published - 1987

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abstract = "The method applied by Bellomo and Toscani [J. Math. Phys. 26, 334 ( 1985)] for the Boltzmann equation in an infinite medium to establish global results for bounded media with partially absorbing boundary conditions is generalized. The method does not require that the equilibrium solution be the vacuum state and, accordingly, does not rely on positivity/ monotonicity arguments. The growth produced by the nonlinearity is compensated by the combined effect of streaming and (partial) absorption (leakage) at the boundary.",

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AB - The method applied by Bellomo and Toscani [J. Math. Phys. 26, 334 ( 1985)] for the Boltzmann equation in an infinite medium to establish global results for bounded media with partially absorbing boundary conditions is generalized. The method does not require that the equilibrium solution be the vacuum state and, accordingly, does not rely on positivity/ monotonicity arguments. The growth produced by the nonlinearity is compensated by the combined effect of streaming and (partial) absorption (leakage) at the boundary.

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The nonlinear Boltzmann equation with partially absorbing boundary conditions. Global existence and uniqueness results

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