A free boundary problem for cell motility
vendredi 24 janvier 2020, 11h00 - 12h00
In this talk we will present some works in collaboration with Nicolas Meunier et Antoine Mellet (University of Maryland).
I will present a free boundary problem arising from a sharp interface limit of a phase-field model. The phase-field model integrates the most important physical processes involved in cell motility and we provide a rigorous analysis in one dimension. The sharp interface limit leads to a Hele-Shaw type free boundary problem with an additional destabilizing term at the boundary. This terms reflects the active nature of the cell, such as protusion creation. We will present the principal properties arising from a phenomenon of bifurcation with respect to the destabilizing parameter: hysteresis phenomenon and the existence of traveling waves like solutions in one dimension and in two dimensions.