On the stability of homogeneous solutions to some aggregation models

Abstract

Vasculogenesis, i.e. self-assembly of endothelial cellsleading to capillary network formation, has been the object ofmany experimental investigations in recent years, due to itsrelevance both in physiological and in pathological conditions. Weperformed a detailed linear stability analysis of two models ofin vitro vasculogenesis, with the aim of checking theirpotential for structure formation starting from initial datarepresenting a continuum cell monolayer. The first model turns outto be unstable at low cell densities, while pressure stabilizes itat high densities. The second model is instead stable at low celldensities. Detailed information about the instability regions andthe structure of the critical wave numbers are obtained in severalinteresting limiting cases. We expect that altogether, thisinformation will be useful for further comparison of the twomodels with experiments.