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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
10/2009

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

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

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.

Received:
Feb 18, 2009
Published:
Feb 24, 2009

Related publications

inJournal
2010 Repository Open Access
Elio Eduardo Espejo Arenas, Angela Stevens and Juan J. L. Velázquez

A note on non-simultaneous blow-up for a drift-diffusion model

In: Differential and integral equations, 23 (2010) 5/6, pp. 451-462