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Elliptic Carleman Estimates And Applications To Stabilization And Controllability Volume I Dirichlet Boundary Conditions On Euclidean Space Jrme Le Rousseau

Name: Elliptic Carleman Estimates And Applications To Stabilization And Controllability Volume I Dirichlet Boundary Conditions On Euclidean Space Jrme Le Rousseau
SKU: BELL-50597408
Price: 31.00 USD
Availability: InStock
Rating: 4.1 (10 reviews)

SKU: BELL-50597408

Elliptic Carleman Estimates And Applications To Stabilization And Controllability Volume I Dirichlet Boundary Conditions On Euclidean Space Jrme Le Rousseau

$ 31.00 ~~$ 45.00~~ (-31%)

4.1

10 reviews

Elliptic Carleman Estimates And Applications To Stabilization And Controllability Volume I Dirichlet Boundary Conditions On Euclidean Space Jrme Le Rousseau instant download after payment.

Publisher: Birkhäuser

File Extension: PDF

File size: 5.38 MB

Pages: 409

Author: Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano

ISBN: 9783030886738, 3030886735

Language: English

Year: 2022

Product desciption

Elliptic Carleman Estimates And Applications To Stabilization And Controllability Volume I Dirichlet Boundary Conditions On Euclidean Space Jrme Le Rousseau by Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano 9783030886738, 3030886735 instant download after payment.

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.