MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A free boundary problem for cell motion

Jan Fuhrmann and Angela Stevens


The ability of a large variety of eukaryotic cells to actively move along different substrates plays a vital role in many biological processes. A key player in these processes is the cytoskeleton. In [JTB 249, 2007] we introduced a minimal hyperbolic-parabolic model for the reorganization of the actin cytoskeleton of a generic cell resting on a flat substrate and turning into a polarized state upon some external cue. In this paper we derive moving boundary conditions for the same cytoskeleton model and by this allow for the description of actual motion. For the free boundary problem we prove short time well-posedness for a wide class of initial conditions and analyze the emergence of Dirac measures in the densities of actin filament tips. These have a direct biophysical interpretation as sharp polymerization fronts which are experimentally observed by [Ponti et al, 2004], for example. Further, numerical results will illustrate both, the motion of an initially symmetric resting cell and the emergence of sharp fronts of actin filaments from initially smooth distributions.


Related publications

2015 Repository Open Access
Jan Fuhrmann and Angela Stevens

A free boundary problem for cell motion

In: Differential and integral equations, 28 (2015) 7/8, pp. 695-732