| Abstract: |
| Experiments of in vitro vasculogenesis show that endothelial cells randomly distributed on the gel matrix will organize themselves into a connected capillary network. As a kind of taxis, this network aggregation phenomenon of endothelial cells can not be simulated by the classical Keller-Segel model. The viscous vasculogenesis model proposed by the biologist Gamba et al. can model the experimental phenomenon very well. This talk will present a series of studies on the existence and long-time behavior of the solution for viscous vasculogenesis model, including: the stability of rarefaction wave for the Cauchy problem of the one-dimensional viscous vasculogenesis model, the stability of rarefaction wave and the boundary layer for the initial boundary value problem of the one-dimensional viscous vasculogenesis model over $\mathbb{R}^{1}_{+}$, and the stability of planar staionary solution for the initial boundary value problem of the three-dimensional viscous vasculogenesis model over $\mathbb{R}^3_{+}$. |
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