Applications

Abstract

The following chapter is devoted to the study of two industrial applications, in which optimization with partial differential equations plays a crucial role. It shall provide a survey of the different mathematical settings which can be handled with the general optimal control calculus presented in the previous chapters. We focus on large scale optimal control problems involving two well-known types of partial differential equations, namely elliptic and parabolic ones. Since real world applications lead generally to mathematically quite involved problems, we study in particular nonlinear systems of equations. The examples are chosen in such a way that they are up-to-date and modern mathematical tools are used for their specific solution. The industrial fields we cover are modern semiconductor design and glass production. We start each section with a modeling part to introduce the underlying physics and mathematical models, which are then followed by the analytical and numerical study of the related optimal control problems.