Mathematical Analysis of a Model for the Initiation of Angiogenesis

Source abstract

In this paper we consider a nonlinear system of partial differential equations consisting of one parabolic equation and two ordinary differential equations in t. The system arises in a mathematical model of angiogenesis, a process of sprouting of new blood vessels from an existing vascular network. We prove that the system has a unique global solution and study its asymptotic behavior as $t\rightarrow \infty$. In particular, we show that stationary solutions are local attractors.