Substrate-based crawling motility of eukaryotic cells is essential for many biological
functions, both in developing and mature organisms. Motility dysfunctions are involved in …

We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a
biological cell confined between two parallel surfaces. In our model, the cell is driven out of …

We introduce and study a diffuse interface model describing cell motility. We provide a
detailed rigorous analysis of the model in dimension 1 and formally derive the sharp …

In the framework of a phase field model of a single cell crawling on a substrate, we
investigate how the properties of the cell membrane affect the shape and motility of the cell …

In this paper, we prove the existence of traveling wave solutions for an incompressible
Darcy's free boundary problem recently introduced in [6] to describe cell motility. This free …

We study Brakke's mean curvature flow with obstacles and with a right-angle boundary
condition. Assuming that the obstacles have-boundaries, we prove that a weak solution …

We consider a continuous active polar fluid model for the spreading of epithelial monolayers
introduced by R. Alert, C. Blanch-Mercader, and J. Casademunt, 2019. The corresponding …

L. Berlyand et al./CR Acad. Sci. Paris, Ser. I 354 (2016) 986–992 987 comme de brutales
mises en mouvement de la cellule et des oscillations de sa forme. Le modèle consiste en …

We consider the obstacle problem of the weak solution to the mean curvature flow, in the
sense of Brakke's mean curvature flow. We prove the global existence of the weak solution …

The phase-field equations have many attractive characteristics. First, phase separation can
be induced by the phase-field equations. It transforms from a single homogeneous mixture …