A note on the time decay of solutions for the linearized Wigner-Poisson system

Pages: 181 - 189, Volume 2, Issue 1, March 2009

doi:10.3934/krm.2009.2.181       Abstract        Full Text (149.0K)       Related Articles

Irene M. Gamba - Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Texas 78712, United States (email)
Maria Pia Gualdani - Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Texas 78712, United States (email)
Christof Sparber - Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom (email)

Abstract: We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.

Keywords:  Wigner transform, Poisson coupling, Landau damping, plasma physics.
Mathematics Subject Classification:  Primary: 35Q40, 35B20; Secondary: 35B40.

Received: November 2008;      Revised: November 2008;      Published: January 2009.