Differential and Integral Equations

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

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

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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.

Article information

Differential Integral Equations, Volume 23, Number 5/6 (2010), 451-462.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B35: Stability 35B40: Asymptotic behavior of solutions 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations


Espejo, E.E.; Stevens, A.; Velázquez, J.J.L. A Note on non-simultaneous blow-up for a drift-diffusion model. Differential Integral Equations 23 (2010), no. 5/6, 451--462. https://projecteuclid.org/euclid.die/1356019306

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