Nicolas Meunier
(Université Paris V, France)

Analysis of self-organization systems for cell polarization
(Joint work with V. Calvez and R. Voituriez)

In this work, we investigate the dynamics of a modified Keller-Segel type model. On the contrary to the classical configuration, the chemical production term is located on the boundary. In the one-dimensional case and in a particular case in dimension two, we prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass and they blow-up in finite time above the critical mass. Furthermore, in the one-dimensional case, using entropy techniques, we provide quantitative convergence results for the subcritical case. This work is completed with a more realistic model (still one-dimensional) for modeling purpose. In this new setting, the chemical is supplied by a quantity which evolves by exchanging particles at the boundary. Finally some results are given for the two-dimensional case and we also provide some links with cell polarisation that is an essential step for many biological processes and that is involved for instance in cell migration, division, or morphogenesis.