John E. Lagnese - Böcker

The articles in this volume focus on control theory of systems governed by nonlinear linear partial differential equations, identification and optimal design of such systems, and modelling of advanced materials. Optimal design of systems governed by PDEs is a relatively new area of study, now particularly relevant because of interest in optimization of fluid flow in domains of variable configuration, advanced and composite materials studies and "smart" materials which include possibilities for built in sensing and control actuation. The book will be of interest to both applied mathematicians and to engineers.

This monograph considers problems of optimal control for partial differential equa­ tions of elliptic and, more importantly, of hyperbolic types on networked domains. The main goal is to describe, develop and analyze iterative space and time domain decompositions of such problems on the infinite-dimensional level. While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. A keyword in this context is parallelism. This development is perhaps best illustrated by the fact that we just encountered the 15th annual conference precisely on this topic. Without attempting to provide a complete list of introductory references let us just mention the monograph by Quarteroni and Valli [91] as a general up-to-date reference on domain decomposition methods for partial differential equations. The emphasis of this monograph is to put domain decomposition methods in the context of so-called virtual optimal control problems and, more importantly, to treat optimal control problems for partial differential equations and their decom­ positions by an all-at-once approach. This means that we are mainly interested in decomposition techniques which can be interpreted as virtual optimal control problems and which, together with the real control problem coming from an un­ derlying application, lead to a sequence of individual optimal control problems on the subdomains that are iteratively decoupled across the interfaces.