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

Masaki Kurokiba; Toshitaka Nagai; T. Ogawa

doi:10.3934/cpaa.2006.5.97

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2006, Volume 5, Issue 1: 97-106. Doi: 10.3934/cpaa.2006.5.97

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

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

Received: August 31, 2004

Revised: September 30, 2005

Published: February 2006

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Abstract

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.

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Mathematics Subject Classification: Primary 35K15, 35K55, 35Q60; Secondary78A35.

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