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Control of Partial Differential Equations

Cetraro, Italy 2010, Editors: Piermarco Cannarsa, Jean-Michel Coron

  • Book
  • © 2012

Overview

Authors:
  1. Fatiha Alabau-Boussouira

    1. LMAM, Université Paul Verlaine-Metz, Metz, France

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  2. Roger Brockett

    1. Engineering and Applied Sciences, Harvard University, Cambridge, USA

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  3. Olivier Glass

    1. CEREMADE, Université Paris-Dauphine, Paris, France

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  4. Jérôme Le Rousseau

    1. Laboratoire MAPMO, Université d'Orléans, Orléans, France

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  5. Enrique Zuazua

    1. Basque Center for Applied Mathematics, Derio, Spain

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  • Self-contained: the book can be used by researchers in partial differential equations who want to learn about the control of such equations without requiring a special background in control theory.
  • Covers the main recent progress in control of partial differential equations.
  • Includes numerous challenging open problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2048)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. On Some Recent Advances on Stabilization for Hyperbolic Equations

    • Fatiha Alabau-Boussouira
    Pages 1-100

  3. Notes on the Control of the Liouville Equation

    • Roger Brockett
    Pages 101-129

  4. Some Questions of Control in Fluid Mechanics

    • Olivier Glass
    Pages 131-206

  5. Carleman Estimates and Some Applications to Control Theory

    • Jérôme Le Rousseau
    Pages 207-243

  6. The Wave Equation: Control and Numerics

    • Sylvain Ervedoza, Enrique Zuazua
    Pages 245-339

  7. Back Matter

    Pages 341-344
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Keywords

About this book

The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a friendly introduction to, and an updated account of, some of the most active trends in current research.

Authors and Affiliations

  • LMAM, Université Paul Verlaine-Metz, Metz, France

    Fatiha Alabau-Boussouira

  • Engineering and Applied Sciences, Harvard University, Cambridge, USA

    Roger Brockett

  • CEREMADE, Université Paris-Dauphine, Paris, France

    Olivier Glass

  • Laboratoire MAPMO, Université d'Orléans, Orléans, France

    Jérôme Le Rousseau

  • Basque Center for Applied Mathematics, Derio, Spain

    Enrique Zuazua

Bibliographic Information

  • Book Title: Control of Partial Differential Equations

  • Book Subtitle: Cetraro, Italy 2010, Editors: Piermarco Cannarsa, Jean-Michel Coron

  • Authors: Fatiha Alabau-Boussouira, Roger Brockett, Olivier Glass, Jérôme Le Rousseau, Enrique Zuazua

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-27893-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2012

  • Softcover ISBN: 978-3-642-27892-1Published: 20 April 2012

  • eBook ISBN: 978-3-642-27893-8Published: 23 April 2012

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIII, 344

  • Number of Illustrations: 17 b/w illustrations, 49 illustrations in colour

  • Topics: Partial Differential Equations, Systems Theory, Control, Fluid- and Aerodynamics, Numerical Analysis

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