Optimization of a mixing problem with boundary control

The motivation of this study comes from the mixing problem by minimizing the cost through the stirring force exerted on the container wall. First, we introduce the general optimization of mixing of a scalar field such as temperature or salt stirred by Stokes flow. Second, we introduce a boundary control problem and derive the first order necessary condition of optimal solution. Finally, we present a line search method to solve this problem. This is a collaboration with Dr. Weiweihu at University of Georgia.