Date: March, 2022

Book: Optimization and Control for Partial Differential Equations

DOI: https://doi.org/10.1515/9783110695984
 

Chapter 3

Limits of stabilizability for a semilinear model for gas pipeline flow

Martin Gugat, Chair for Dynamics Control and Numerics – Alexander von Humboldt Prof. FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Michael Herty, RWTH Aachen University.

Chapter 12

12 Numerical issues and turnpike phenomenon in optimal shape design

Gontran Lance, Sorbonne Université, Laboratoire Jacques-Louis Lions, CNRS
Emmanuel Trélat, Sorbonne Université, Laboratoire Jacques-Louis Lions, CNRS
Enrique Zuazua, Chair for Dynamics Control and Numerics – Alexander von Humboldt Prof. FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Preface

“The optimist proclaims that we live in the best of all possible worlds;
and the pessimist fears this is true.”
-James Branch Cabell, The Silver Stallion

Over the last century, our information society has witnessed the emergence of a new method of scientific inquiry underpinned by Applied Mathematics. Our understanding of complex systems such as the Earth’s weather, the financial market, or social networks, to name a few, is based around mathematical modeling, simulation, and optimization. Modeling and simulation deal with an accurate identification and replication of the underlying processes. Optimization addresses the characterization and computation of actions to achieve a best possible outcome. Mathematical optimization has been present throughout the history of humankind. From Queen Dido’s legend and the isoperimetric problem, going through Fermat’s principle of least time in 1662, until the 20th century development of optimal control theory by Bellman and Pontryagin, the synthesis of optimal actions has been a formidable mathematical challenge.

 
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Image: Book cover (De Gruyter)

Herzog, Roland, Heinkenschloss, Matthias, Kalise, Dante, Stadler, Georg and Trélat, Emmanuel. Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization, Berlin, Boston: De Gruyter, 2022. https://doi.org/10.1515/9783110695984

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