Interest in the area of control of systems defined by partial differential Equations has increased strongly in recent years. A major reason has been the requirement of these systems for sensible continuum mechanical modelling and optimization or control techniques which account for typical physical phenomena. Particular examples of problems on which substantial progress has been made are the control and stabilization of mechatronic structures, the control of growth of thin films and crystals, the control of Laser and semi-conductor devices, and shape optimization problems for turbomachine blades, shells, smart materials and microdiffractive optics. This volume contains original articles by world reknowned experts in the fields of optimal control of partial differential equations, shape optimization, numerical methods for partial differential equations and fluid dynamics, all of whom have contributed to the analysis and solution of many of the problems discussed. The collection provides a state-of-the-art overview of the most challenging and exciting recent developments in the field. It is geared towards postgraduate students and researchers dealing with the theoretical and practical aspects of a wide variety of high technology problems in applied mathematics, fluid control, optimal design, and computer modelling.

The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.

The international Conference on Optimal Control of Coupled Systems of Partial Di?erential Equations was held at the Mathematisches Forschungsinstitut Ob- wolfach (www.mfo.de) from April, 17 to 23, 2005. The scienti?c program included 30 talks coveringvarious topics as controllability,feedback-control,optimality s- tems, model-reduction techniques, analysis and optimal control of ?ow problems and ?uid-structure interactions, as well as problems of shape and topology op- mization. The applications discussed during the conference range from the op- mization and control of quantum mechanical systems, the design of piezo-electric acoustic micro-mechanical devices, optimal control of crystal growth, the control of bodies immersed into a ?uid to airfoil design and much more. Thus the app- cations are across all time and length scales. Optimization and control of systems governed by partial di?erential eq- tions and more recently by variational inequalities is a very active ?eld of research in Applied Mathematics, in particular in numerical analysis, scienti?c comp- ing and optimization. In order to able to handle real-world applications, scalable and parallelizable algorithms have to be designed, implemented and validated. This requires an in-depth understanding of both the theoretical properties and the numerical realization of such structural insights. Therefore, a 'core' devel- ment within the ?eld of optimization with PDE-constraints such as the analysis of control-and-state-constrained problems, the role of obstacles, multi-phases etc. and an interdisciplinary 'diagonal' bridging regarding applications and numerical simulation are most important.

This Teubner-Text contains selected contributions to the "10th Conference on Problems and Methods in Mathematical Physics (10th TMP)", held at the Technical University of Chemnitz-Zwickau in Chemnitz, Germany, September 13 - 17, 1993. The main topics of the conference were Scientific Computing in Solid and Fluid Mechanics Problems with Singularities Boundary Integral Methods Multilevel Finite Element Methods Free Boundary Value Problems and Optimal Control Numerical Functional Analysis. The conference brought together more than 170 experts from 17 countries, and the 18 plenary and invited lectures as well as the 120 short lectures were devo- ted to plenty of problems and latest results in applied mathematical research. Undoubtedly, the majority of these contributions would have deserved publi- cation. However, this volume does not intend to reflect the whole scientific contents of the conference in the usual form of proceedings. It is rather aiming at giving a survey of some recent trends in fields covered by the topics of this meeting. The organizing committee hopes that this Teubner-Text reflects the main spirit of the 10th TMP.

Die mathematische Theorie der optimalen Steuerung hat sich im Zusammenhang mit Berechnungen fur die Luft- und Raumfahrt schnell zu einem wichtigen und eigenstandigen Gebiet der angewandten Mathematik entwickelt. Die optimale Steuerung durch partielle Differentialgleichungen modellierter Prozesse wird eine numerische Herausforderung der Zukunft sein. Im Buch werden entsprechende Grundlagen mit langsam steigendem Schwierigkeitsgrad entwickelt. Es enthalt viele Beispiele und eignet sich als Grundlage fur Vorlesungen und Seminare.
Der Text wurde fur die 2. Auflage grundlegend uberarbeitet. Die Darstellung der numerischen Methoden orientiert sich starker an den konkret zu rechnenden Systemen. Neueste Ergebnisse zur maximalen Regularitat parabolischer Differentialgleichungen sind eingearbeitet.
Losungshinweise zu den Ubungsaufgaben findet der Studierende nun im OnlinePLUS-Service des Verlages.
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