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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Submitted on : Monday, May 23, 2011 - 10:12:09 AM
Last modification on : Wednesday, November 20, 2019 - 7:47:55 AM
Long-term archiving on: Wednesday, August 24, 2011 - 2:21:50 AM

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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. 2011. ⟨hal-00594777⟩

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