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January  2009, 24(1): 13-33. doi: 10.3934/dcds.2009.24.13

Propagation of singularities for classical solutions of the Vlasov-Poisson-Boltzmann equation

Laurent Bernis 1, and  Laurent Desvillettes 2,

1. 

Université d’Orléans, MAPMO, CNRS, BP 6759, 45067 Orléans Cedex 2, France
2. 

ENS Cachan, CMLA, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt Wilson, 94235 Cachan Cedex

Received  June 2007 Revised  December 2007 Published  January 2009

In this work, we prove that the singularities (in a fractional Sobolev space) of the classical solutions of the Vlasov-Poisson-Boltzmann equation are propagated along the characteristics of the Vlasov-Poisson equation, and decay exponentially.
Keywords: Propagation of Singularities., Boltzmann Equation, Averaging Lemma, Vlasov Equation.
Mathematics Subject Classification: 76P05, 35B65, 76X05, 82C4.
Citation: Laurent Bernis, Laurent Desvillettes. Propagation of singularities for classical solutions of the Vlasov-Poisson-Boltzmann equation. Discrete & Continuous Dynamical Systems, 2009, 24 (1) : 13-33. doi: 10.3934/dcds.2009.24.13
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