Long-time behavior of an angiogenesis model with flux at the tumor boundary

Details Long-time behavior of an angiogenesis model with flux at the tumor boundary Long-time behavior of an angiogenesis model with flux at the tumor boundary

2012-02-21

arxiv.org/abs/1202.4695v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behaviour of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.

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