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1996 Uniqueness for the BGK-equation in $\mathbb{R}^N$ and rate of convergence for a semi-discrete scheme
Stéphane Mischler
Differential Integral Equations 9(5): 1119-1138 (1996).

Abstract

We prove estimates, in weighted $L^\infty$ spaces, for solutions of the BGK equation in the whole space and lower bound on the associated macroscopic density. $L^\infty$ bound on the macroscopic object $\rho, u$ and $T$ are deduced. Then we may show uniqueness of the solution of the BGK equation with $L^\infty$-bound assumption on the initial data, propagation of estimates on derivatives. As an application, with a BV-bound assumption on the initial data we get the convergence with rate $(\Delta t)^{1/2}$ of a time semi-discretized scheme to the solution.

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Stéphane Mischler. "Uniqueness for the BGK-equation in $\mathbb{R}^N$ and rate of convergence for a semi-discrete scheme." Differential Integral Equations 9 (5) 1119 - 1138, 1996.

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0852.76083
MathSciNet: MR1392097

Subjects:
Primary: 82C40
Secondary: 65M06 , 76P05

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 5 • 1996
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