Liquid multiphase processes represent a promising option for realizing novel, efficient, and sustainable production processes, as required for the transformation towards climate-neutral manufacturing processes. This volume presents the results obtained over twelve years in the DFG-funded collaborative project Transregio 63 "Integrated Chemical Processes in Liquid Multiphase Systems". In an interdisciplinary approach to the design and operation of such processes, essential principles of Green Chemistry are realized, such as using long-chain olefins as model representatives of renewable raw materials, highly effi cient catalysts, and green solvents, linked with process optimization to improve energy and material efficiency. Experts from different fields addressed all steps of the development process, from the description of the reactions on the molecular level via thermodynamics and the design of efficient separation processes to the operation of entire miniplants for liquid multiphase production processes. Thus, the complete development chain from the first reaction-related investigations in the laboratory to the technological realization in miniplants with model-based control is demonstrated. Numerous methodological innovations are proposed and validated using several innovative phase systems (thermomorphic multiphase systems, microemulsion systems, Pickering emulsions) and homogeneously catalyzed reactions. Engineers and chemists from the chemical industry as well as advanced students and researchers will get valuable insights into the physico-chemical phenomena in chemical multiphase processes and benefit from recommendations concerning methods for the selection of phase systems and rapid model-based process development.

Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on "Optimization with Partial Differential Equations" from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on "Constrained Optimization, Identification and Control", "Shape and Topology Optimization", "Adaptivity and Model Reduction", "Discretization: Concepts and Analysis" and "Applications". Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on "Optimization with Partial Differential Equations" from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on "Constrained Optimization, Identification and Control", "Shape and Topology Optimization", "Adaptivity and Model Reduction", "Discretization: Concepts and Analysis" and "Applications". Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

Gegenstand des Buches ist die Bestimmung der bestmoglichen erreichbaren Regelgute in linearen zeitinvarianten Regelkreisen. Hierbei werden keine Einschrankungen bezuglich der Struktur der Regelstrecke oder der Regler gemacht. Ausgangspunkt der Untersuchungen ist eine praxisnahe Spezifikation des gewunschten Regelkreisverhaltens, die Stabilitat, gutes Folgeverhalten und Robustheit sicherstellt, in Form von Schranken fur bestimmte Frequenzgange des geschlossenen Regelkreises. Es wird dann schrittweise die mathematische Theorie entwickelt, mit der sich die Einhaltbarkeit solcher Spezifikationen fur ein gegebenes Streckenmodell uberprufen und die optimale Regelgute ermitteln lasst. Dies geschieht zunachst ausfuhrlich fur zeitkontinuierliche Eingrossenregelkreise. Mit Hilfe einer neu entwickelten Methode zur numerischen Auswertung der resultierenden Bedingungen wurden erstmals fur die wichtigsten Streckentypen Diagramme berechnet, die exakt die notwendigen Kompromisse bei der Regelkreisspezifikation angeben. Unter Benutzung der w-Transformation werden die Ergebnisse auf zeitdiskrete Regelungen ubertragen. Eine knappe Darstellung der Verallgemeinerung der Methodik auf Mehrgrossenregelungen bildet den Abschluss des Buches. Da die erforderliche Robustheit des Regelkreises Bestandteil der Spezifikation ist, liefert die dargestellte Theorie auch eine Aussage daruber, ob fur ein konkretes Problem festeingestellte lineare Regler ausreichend sind, oder ob zu komplexeren Regelungen (nicht-linear, schaltend, adaptiv) ubergegangen werden muss, um die geforderte Regelgute zu erreichen.