Asymptotic evolution of lipid vesicles

Abstract

Dynamics of lipid vesicles is governed by an equation that offers many challenging mathematical problems, still not completely solved. In this paper we study vesicle dynamics by way of example. In a two-dimensional setting, when the vesicle is imagined as a closed curve, we draw a comparison with motion by curvature: it is shown that different decay laws govern the asymptotic relaxation to a circle. Finally, when the vesicle is modelled as an axisymmetric, compact surface, we study its relaxation to a sphere, to obtain the asymptotic shape and to illustrate the difficulties involved in dealing with this kind of evolution.