Optimal Shape Design for Parabolic System and Two-Phase Stefan Problem

Abstract

In this paper we consider the application of the domain control theory in parabolic systems for the approximation of two-phase one-dimensional Stefan problem [1]. In this approach the role of the control function is carried out by the free-boundary (or interface). We use the shape penalty method [2,3] and investigate the corresponding approximation family of control bilinear systems and prove the theorem about uniform approximation. It is shown that classical solution of Stefan problem is a limit of the approximation solutions.