On the Vlasov-Poisson-Fokker-Planck      equation near Maxwellian

Hyung Ju Hwang; Juhi Jang

doi:10.3934/dcdsb.2013.18.681

Article Contents

2013, Volume 18, Issue 3: 681-691. Doi: 10.3934/dcdsb.2013.18.681

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On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian

Hyung Ju Hwang^1, and
Juhi Jang^2,

1.
Department of Mathematics, Pohang University of Science and Technology, Pohang, Gyeongbuk
2.
Department of Mathematics, University of California, Riverside, Riverside, CA 92521

Received: August 31, 2012

Revised: August 31, 2012

Published: April 2013

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Abstract

We establish the exponential time decay rate of smooth solutions of small amplitude to the Vlasov-Poisson-Fokker-Planck equations to the Maxwellian both in the whole space and in the periodic box via the uniform-in-time energy estimates and also the macroscopic equations.

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Mathematics Subject Classification: Primary: 35Q84; Secondary: 82D10.

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