An angiogenesis model with nonlinear chemotactic response and flux at the tumor boundary

In this paper we consider a parabolic problem as well as its stationary counterpart of a model arising in angiogenesis. The problem includes a chemotaxis type term and a nonlinear boundary condition at the tumor boundary. We show that the parabolic problem admits a unique positive global in time solution. Moreover, by bifurcation methods, we show the existence of coexistence states and also we study the local stability of the semi-trivial states.