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Abstract
Vasculogenesis, i.e. self-assembly of endothelial cells
leading to capillary network formation, has been the object of
many experimental investigations in recent years, due to its
relevance both in physiological and in pathological conditions. We
performed a detailed linear stability analysis of two models of
in vitro vasculogenesis, with the aim of checking their
potential for structure formation starting from initial data
representing a continuum cell monolayer. The first model turns out
to be unstable at low cell densities, while pressure stabilizes it
at high densities. The second model is instead stable at low cell
densities. Detailed information about the instability regions and
the structure of the critical wave numbers are obtained in several
interesting limiting cases. We expect that altogether, this
information will be useful for further comparison of the two
models with experiments.
Mathematics Subject Classification: 92D25, 76E99.
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