Article ID Journal Published Year Pages File Type
1708884 Applied Mathematics Letters 2012 5 Pages PDF
Abstract

For a class of drift–diffusion systems Kurokiba et al. [M. Kurokiba, T. Nagai, T. Ogawa, The uniform boundedness and threshold for the global existence of the radial solution to a drift–diffusion system, Commun. Pure Appl. Anal. 5 (2006) 97–106.] proved global existence and uniform boundedness of the radial solutions when the L1L1-norm of the initial data satisfies a threshold condition. We prove in this letter that this result prescribes a region in the plane of masses which is sharp in the sense that if the drift–diffusion system is initiated outside the threshold region of global existence, then blow-up is possible: suitable initial data can be built up in such a way that the corresponding solution blows up in a finite time.

Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
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