Elliptic Carleman Estimates and Applications to Stabilization and C...
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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I

Dirichlet Boundary Conditions on Euclidean Space

Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano


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This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.  All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds.

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.

About the book
Author
Jérôme  Le Rousseau , Gilles  Lebeau , Luc  Robbiano
Imprint
Birkhäuser
Collection
Progress in Nonlinear Differential Equations and Their Applications
Publication date
2022-03-28
Pages
411 pages
Print ISBN
9783030886738
Language
English
Ebook informations
EAN PDF
9783030886745
Price
£119.50
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Copy count 4
Print count 41
File size 5673 Ko
Ce livre est accessible aux handicaps   Informations accessibility
EAN EPUB
9783030886745
Price
£119.50
Read more
Copy count 4
Print count 41
File size 35912 Ko
Ce livre est accessible aux handicaps   Informations accessibility
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