Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 425-434 |
| Journal / Publication | Journal of Mathematical Analysis and Applications |
| Volume | 327 |
| Issue number | 1 |
| Publication status | Published - 1 Mar 2007 |
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Abstract
In this paper, we study the existence of stationary solutions to the Vlasov-Poisson-Boltzmann system when the background density function tends to a positive constant with a very mild decay rate as | x | → ∞. In fact, the stationary Vlasov-Poisson-Boltzmann system can be written into an elliptic equation with exponential nonlinearity. Under the assumption on the decay rate being (ln (e + | x |))- α for some α > 0, it is shown that this elliptic equation has a unique solution. This result generalizes the previous work [R. Glassey, J. Schaeffer, Y. Zheng, Steady states of the Vlasov-Poisson-Fokker-Planck system, J. Math. Anal. Appl. 202 (1996) 1058-1075] where the decay rate (1 + | x |)- frac(1, 2) is assumed. © 2006 Elsevier Inc. All rights reserved.
Research Area(s)
- Nonlinear elliptic equation, Stationary solutions, Vlasov-Poisson-Boltzmann system
Citation Format(s)
Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system. / Duan, Renjun; Yang, Tong; Zhu, Changjiang.
In: Journal of Mathematical Analysis and Applications, Vol. 327, No. 1, 01.03.2007, p. 425-434.
In: Journal of Mathematical Analysis and Applications, Vol. 327, No. 1, 01.03.2007, p. 425-434.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
