A note on non-simultaneous blow-up for a drift-diffusion model. (English) Zbl 1240.35230

Espejo, E. E.; Stevens, A.; Velázquez, J. J. L.

Differ. Integral Equ. 23, No. 5-6, 451-462 (2010).

Summary: 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. We also 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.

MSC:

35K45	Initial value problems for second-order parabolic systems
35B44	Blow-up in context of PDEs
35K55	Nonlinear parabolic equations

Keywords:

drift-diffusion model; non-simultaneous blow-up; parabolic-elliptic