A Mathematical Approach in the Design of Arterial Bypass Using Unsteady Stokes Equations

In this paper we apply optimal control for the shape optimization of aortocoronaric bypass anastomoses [8]. We analyze the “first correction” method which is derived by applying a perturbation method to the initial unsteady problem in a space-time domain Ω×(0, T ) with Ω ⊂ R. The boundary ∂Ω of Ω is parameterized by a suitable function f . Then we propose numerical methods for its solution. Optimal control (Lions [4]) by perturbation theory (Van Dyke [17]) using adjoint equation techniques (Agoshkov [1] and Marchuk [6]) provides a tool