  When it is polarised, a cell develops an asymmetric distribution of specific
molecular markers, cytoskeleton and cell membrane shape. Polarisation can occur
spontaneously or be triggered by external signals, like gradients of signalling
molecules... In this work, we use the published models of cell polarisation and
we set a numerical analysis for these models. They are based on nonlinear
convection-diffusion equations and the nonlinearity in the transport term
expresses the positive loop between the level of protein concentration
localised in a small area of the cell membrane and the number of new proteins
that will be convected to the same area. We perform numerical simulations and
we illustrate that these models are rich enough to describe the apparition of a
polarisome.

Analysis of PDEs