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March  2009, 2(1): 181-189. doi: 10.3934/krm.2009.2.181

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

Irene M. Gamba 1, , Maria Pia Gualdani 1, and  Christof Sparber 2,

1. 

Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Texas 78712, United States, United States
2. 

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Received  November 2008 Revised  November 2008 Published  January 2009

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: plasma physics., Poisson coupling, Wigner transform, Landau damping.
Mathematics Subject Classification: Primary: 35Q40, 35B20; Secondary: 35B4.
Citation: Irene M. Gamba, Maria Pia Gualdani, Christof Sparber. A note on the time decay of solutions for the linearized Wigner-Poisson system. Kinetic & Related Models, 2009, 2 (1) : 181-189. doi: 10.3934/krm.2009.2.181
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