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

By Elio Espejo, Angela Stevens, Juan J. López Velázquez. Differential and Integral Equations, 2010

47 citations recorded by the source corpus.

In this paper, we consider a drift-diusion model of parabo- lic-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-diusion model in this paper, for which blow-up happens, is larger than suggested by previous results in the literature. u1(0;x) = u1;0(x) 0; u2(0;x) = u2;0(x) 0; x2 R 2 ;

Subfields: Computational Theory and Mathematics, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/3dfca6286c57168827af7c36fddd730ffffdc766

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Citations in the corpus

Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant (2015, background): “More recently, systems of two species with one chemoattractant have been studied by different research groups, the flnite-time blow-up in bounded domains for the ParabolicParabolic-Elliptic issue has been analyzed by Espejo, Stevens and Velázquez [7] and [8] for simultaneous and non-simultaneous blo”
Stabilization in a two-species chemotaxis system with a logistic source (2012, background): “Motivated by the question whether multi-species chemotaxis mechanisms can be responsible for processes of cell sorting, the latter work focuses on the occurrence of blow-up phenomena and asymptotic behaviour of such unbounded solutions (see also [4, 5] for the case when χ1 and χ2 have different sign”