Analysis of a non local model for spontaneous cell polarisation

Abstract : In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We characterize the following behaviours in the one-dimensional case: solutions are global if the mass is below the critical mass and they blow-up in finite time above the critical mass. The higher-dimensional case is also discussed. The results are reminiscent of the classical Keller-Segel system in double the dimension. In addition, in the one-dimensional case we prove quantitative convergence results using relative entropy techniques. This work is complemented with a more realistic model that takes into account dynamical exchange of molecular content at the boundary. In the one-dimensional case we prove that blow-up is prevented. Furthermore, density converges towards a non trivial stationary configuration.
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Pré-publication, Document de travail
MAP5 2012-15. 30 pages. 2011
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https://hal.archives-ouvertes.fr/hal-00594777
Contributeur : Vincent Calvez <>
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Dernière modification le : mardi 17 janvier 2017 - 15:35:56
Document(s) archivé(s) le : mercredi 24 août 2011 - 02:21:50

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  • HAL Id : hal-00594777, version 1
  • ARXIV : 1105.4429

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Vincent Calvez, Rhoda Hawkins, Nicolas Meunier, Raphael Voituriez. Analysis of a non local model for spontaneous cell polarisation. MAP5 2012-15. 30 pages. 2011. <hal-00594777>

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