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Sharp condition for blow-up and global existence in a two species chemotactic Keller–Segel system in 2

Published online by Cambridge University Press:  07 December 2012

ELIO ESPEJO ,
KARINA VILCHES  and
CARLOS CONCA
ELIO ESPEJO
Affiliation:
Department of Mathematics, Technion, 32000 Haifa, Israel email: eespejo@techunix.technion.ac.il
KARINA VILCHES
Affiliation:
Departamento de Ingeniería Matemática (DIM) and Centro de Modelamiento Matemático (CMM), Universidad de Chile (UMI CNRS 2807), Casilla 170-3, Correo 3, Santiago, Chile email: kvilches@dim.uchile.cl
CARLOS CONCA
Affiliation:
Departamento de Ingeniería Matemática (DIM) and Centro de Modelamiento Matemático (CMM), Universidad de Chile (UMI CNRS 2807), Casilla 170-3, Correo 3, Santiago, Chile email: kvilches@dim.uchile.cl Institute for Cell Dynamics and Biotechnology: A Centre for Systems Biology, University of Chile, Santiago, Chile email: cconca@dim.uchile.cl
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Abstract

For the parabolic–elliptic Keller–Segel system in 2 it has been proved that if the initial mass is less than 8π/χ, a global solution exists, and in case the initial mass is larger than 8π/χ, blow-up happens. The case of several chemotactic species introduces an additional question: What is the analog for the critical mass obtained for the single species system? We find a threshold curve in the two species case that allows us to determine if the system is a blow-up or a global in time solution. No radial symmetry is assumed.

Keywords

chemotaxismulticomponent Keller–Segel modelsharp conditions

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 2 , April 2013 , pp. 297 - 313
Copyright
Copyright © Cambridge University Press 2012

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