Propagation of singularities for classical solutions of theVlasov-Poisson-Boltzmann equation

Laurent Bernis; Laurent Desvillettes

doi:10.3934/dcds.2009.24.13

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2009, Volume 24, Issue 1: 13-33. Doi: 10.3934/dcds.2009.24.13

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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
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

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Abstract

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.

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Mathematics Subject Classification: 76P05, 35B65, 76X05, 82C40.

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