# American Institute of Mathematical Sciences

May  2013, 18(3): 681-691. doi: 10.3934/dcdsb.2013.18.681

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

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

Received  September 2012 Revised  September 2012 Published  December 2012

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.
Citation: Hyung Ju Hwang, Juhi Jang. On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 681-691. doi: 10.3934/dcdsb.2013.18.681
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