The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system

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March 2006, 5(1): 97-106. doi: 10.3934/cpaa.2006.5.97

The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system

Masaki Kurokiba ^1, , Toshitaka Nagai ^2, and T. Ogawa ^3,

1.	Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan
2.	Graduate School of Mathematics, Hiroshima University, Hiroshima, 739-8526, Japan
3.	Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578

Received September 2004 Revised October 2005 Published December 2005

Abstract
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In this paper, we discuss the global existence and uniform boundedness of the radial solutions to the drift-diffusion system in two space dimension, which is derived from the simulation of semiconductor device design and self-interacting particles. It is shown that the time global existence and the uniform boundedness of the solution to the problem below the sharp threshold condition.

Keywords: radial solution, Drift-diffusion system, threshold condition., uniform boundedness.

Mathematics Subject Classification: Primary 35K15, 35K55, 35Q60; Secondary78A3.

Citation: Masaki Kurokiba, Toshitaka Nagai, T. Ogawa. The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system. Communications on Pure & Applied Analysis, 2006, 5 (1) : 97-106. doi: 10.3934/cpaa.2006.5.97

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