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February  2004, 4(1): 203-220. doi: 10.3934/dcdsb.2004.4.203

On the stability of homogeneous solutions to some aggregation models

R. Kowalczyk 1, , A. Gamba 1, and  L. Preziosi 1,

1. 

Department of Mathematics, Politecnico, Torino, Italy, Italy, Italy

Received  November 2002 Revised  June 2003 Published  November 2003

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.
Keywords: Burgers' equation., Angiogenesis.
Mathematics Subject Classification: 92D25, 76E9.
Citation: R. Kowalczyk, A. Gamba, L. Preziosi. On the stability of homogeneous solutions to some aggregation models. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 203-220. doi: 10.3934/dcdsb.2004.4.203
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