Overview
- 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
Keywords
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
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