Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I - Dirichlet Boundary Conditions on Euclidean Space (Hardcover, 1st ed. 2022)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Progress in Nonlinear Differential Equations and Their Applications, 97
Release date:	March 2022
First published:	2022
Authors:	Jerome Le Rousseau • Gilles Lebeau • Luc Robbiano
Dimensions:	254 x 178mm (L x W)
Format:	Hardcover
Pages:	411
Edition:	1st ed. 2022
ISBN-13:	978-3-03-088673-8
Categories:	Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN:	3-03-088673-5
Barcode:	9783030886738

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