A Note on Non-Simultaneous Blow-up for a Drift-Diffusion Model

Elio Eduardo Espejo, Angela Stevens, and Juan J.L. Velazquez

Contact the author: Please use for correspondence this email.
Submission date: 18. Feb. 2009
Pages: 17
published in: Differential and integral equations, 23 (2010) 5/6, p. 451-462 
Bibtex
Download full preprint: PDF (672 kB)

Abstract:
In this paper we consider a drift-diffusion model of parabolic-elliptic type, with three coupled equations. We prove that there exist parameter regimes for which non-simultaneous blow-up of solutions happens. This is in contrast to a two-chemotactic species model, coupled to an elliptic equation for an attractive chemical produced by the two species, where blow-up of one species implies blow-up of the other one at the same time. Also, we show that the range of parameters of the drift-diffusion model in this paper, for which blow-up happens, is larger than suggested by previous results in the literature.