Global solutions to the relativistic Vlasov-Poisson-Fokker-Planck system

Lan  Luo; Hongjun Yu

doi:10.3934/krm.2016.9.393

Article Contents

2016, Volume 9, Issue 2: 393-405. Doi: 10.3934/krm.2016.9.393

This issue Previous Article An accurate and efficient discrete formulation of aggregation population balance equation Next Article Parameter extraction of complex production systems via a kinetic approach

Global solutions to the relativistic Vlasov-Poisson-Fokker-Planck system

Lan Luo^1, and
Hongjun Yu^2,

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
2.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631

Received: July 2015

Revised: September 2015

Published: June 2016

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Abstract

Global solutions to the relativistic Vlasov-Poisson-Fokker-Planck system near the relativistic Maxwellian are constructed based on an approach by combining the compensating function and energy method. In addition, an exponential rate in time of the solution to its equilibrium is obtained.

Keywords:

The relativistic Vlasov-Poisson-Fokker-Planck system,
global solution,
exponential decay,
compensating function,
energy method.

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

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References

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