Authors:
- Explores applications of Carleman estimates to study stabilization and controllability properties of PDEs
- Covers necessary background material in detail
- Complemented by a second volume that considers Carleman estimates in Euclidean space
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 97)
Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)
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Table of contents (12 chapters)
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Front Matter
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Calculus with a Large Parameter, Carleman Estimates Derivation
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Front Matter
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Applications of Carleman Estimates
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Front Matter
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Background Material: Analysis and Evolution Equations
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Front Matter
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Back Matter
About this book
The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.
Authors and Affiliations
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Laboratoire analyse, géométrie et applications, Université Sorbonne Paris-Nord, Université Paris 8, Villetaneuse, France
Jérôme Le Rousseau
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Laboratoire Jean Dieudonné, Université de Nice Sophia-Antipolis, Nice, France
Gilles Lebeau
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Laboratoire de Mathématiques de Versailles, Université Paris-Saclay, UVSQ, CNRS, Versailles, France
Luc Robbiano
Bibliographic Information
Book Title: Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
Book Subtitle: Dirichlet Boundary Conditions on Euclidean Space
Authors: Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-030-88674-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-88673-8Published: 29 March 2022
Softcover ISBN: 978-3-030-88676-9Published: 30 March 2023
eBook ISBN: 978-3-030-88674-5Published: 28 March 2022
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: VIII, 411
Number of Illustrations: 8 b/w illustrations, 20 illustrations in colour
Topics: Analysis, Systems Theory, Control, Operator Theory, Functional Analysis