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September 2007 The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$
Renjun Duan
Methods Appl. Anal. 14(3): 227-250 (September 2007).


In this paper, we review some recent results on the Boltzmann equation near the equilibrium states in the whole space $\mathbb R^n$. The emphasize is put on the well-posedness of the solution in some Sobolev space without time derivatives and its uniform stability and optimal decay rates, and also on the existence and asymptotical stability of the time-periodic solution. Most of results obtained here are proved by combining the energy estimates and the spectral analysis.


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Renjun Duan. "The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$." Methods Appl. Anal. 14 (3) 227 - 250, September 2007.


Published: September 2007
First available in Project Euclid: 24 October 2008

zbMATH: 1157.76042
MathSciNet: MR2459826

Primary: 76P05 , 82C40 , 82D05

Keywords: Boltzmann equation , energy estimates , equilibrium state

Rights: Copyright © 2007 International Press of Boston

Vol.14 • No. 3 • September 2007
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