Threshold condition for global existence and blow-up to a radially symmetric drift-diffusion system

Carlos Conca, Elio Espejo

Research output: Journal PublicationArticlepeer-review

17 Citations (Scopus)

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) 97106.] proved global existence and uniform boundedness of the radial solutions when the L1-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.

Original languageEnglish
Pages (from-to)352-356
Number of pages5
JournalApplied Mathematics Letters
Volume25
Issue number3
DOIs
Publication statusPublished - Mar 2012
Externally publishedYes

Keywords

  • Blow-up
  • Driftdiffusion
  • Parabolic equations
  • Threshold condition

ASJC Scopus subject areas

  • Applied Mathematics

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