Blowup threshold and collapse mass separation for a drift-diffusion system in space-dimension two

Elio E. Espejo; Masaki Kurokiba; Takashi Suzuki

doi:10.3934/cpaa.2013.12.2627

Article Contents

2013, Volume 12, Issue 6: 2627-2644. Doi: 10.3934/cpaa.2013.12.2627

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Blowup threshold and collapse mass separation for a drift-diffusion system in space-dimension two

1.
Departamento de Matemáticas, Universidad de los Andes, Bogotá
2.
Muroran Institute of Technology, 27-1 Mizumoto, Muroran, 050-8585
3.
Division of Mathematical Science, Department of System Innovation, Graduate School of Engineering Science, Osaka University, 1-3 Machikane-yama, Toyonaka, Osaka, 560-8531

Received: July 31, 2012

Revised: December 31, 2012

Published: October 2013

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Abstract

We study a drift-diffusion system on bounded domain in two-space dimension. This model is provided with a hetero-separative and homo-aggregative feature subject to a gradient of physical or chemical potential which is proportional to their densities. We extend a criterion of global-in-time existence of the solution, especially for non-radially symmetric case. Then we perform the blowup analysis such as the formation of collapses and collapse mass separations. A slightly different model describing cross chemotaxis is also discussed.

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Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 92C15, 92C17.

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