The class of well-posed infinite-dimensional linear systems considered in this paper was introduced by Salamon and Weiss in the 80's. The aim was to provide an axiomatic framework to formulate and solve control problems for systems described by delay and partial differential equations. In this article, this class and its system theoretic properties are described, and an overview of applications of this approach to solving a variety of control problems is given.
The Czochralski process is well known as a practical approach to producing monocrystals from molten semiconductor material. In this paper, we propose a thermal-capillary model with given desired geometry for Czochralski process, and we analyze it from the mathematical point of view. Actually we consider an enthalpy formulation of the model, which is a parabolic variational problem defined over a time-dependent domain, and we give a related existence result with some comments.