TY - JOUR
T1 - Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system
AU - Duan, Renjun
AU - Yang, Tong
AU - Zhu, Changjiang
PY - 2007/3/1
Y1 - 2007/3/1
N2 - 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.
AB - 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.
KW - Nonlinear elliptic equation
KW - Stationary solutions
KW - Vlasov-Poisson-Boltzmann system
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U2 - 10.1016/j.jmaa.2006.04.047
DO - 10.1016/j.jmaa.2006.04.047
M3 - 21_Publication in refereed journal
VL - 327
SP - 425
EP - 434
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -