國立高雄大學圖資館 |

Language: English

Back

Elliptic carleman estimates and applications to stabilization and controllability.Volume I,Dirichlet boundary conditions on Euclidean space

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elliptic carleman estimates and applications to stabilization and controllability.by Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano.
remainder title:	Dirichlet boundary conditions on Euclidean space
Author:	Le Rousseau, Jerome.
other author:	Lebeau, Gilles.
Published:	Cham :Springer International Publishing :2022.
Description:	viii, 411 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Carleman theorem.
Online resource:	https://doi.org/10.1007/978-3-030-88674-5
ISBN:	9783030886745$q(electronic bk.)

Elliptic carleman estimates and applications to stabilization and controllability.Volume I,Dirichlet boundary conditions on Euclidean space
Le Rousseau, Jerome.

Elliptic carleman estimates and applications to stabilization and controllability.Volume I,Dirichlet boundary conditions on Euclidean space[electronic resource] /Dirichlet boundary conditions on Euclidean spaceby Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano. - Cham :Springer International Publishing :2022. - viii, 411 p. :ill. (some col.), digital ;24 cm. - Progress in nonlinear differential equations and their applications,v. 971421-1750 ;. - Progress in nonlinear differential equations and their applications ;v.83..

Introduction -- Part 1: Calculus with a Large Parameter, Carleman Estimates Derivation -- (Pseudo-)differential Operators with a Large Parameter -- Carleman Estimate for a Second-Order Elliptic Operator -- Optimality Aspects of Carleman Estimates -- Part 2: Applications of Carleman Estimates -- Unique Continuation -- Stabilization of the Wave Equation with an Inner Damping -- Controllability of Parabolic Equations -- Part 3: Background Material: Analysis and Evolution Equations -- A Short Review of Distribution Theory -- Invariance under Change of Variables -- Elliptic Operator with Dirichlet Data and Associated Semigroup -- Some Elements of Functional Analysis -- Some Elements of Semigroup Theory -- Bibliography -- Subject Index -- Index of Notation.

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.

ISBN: 9783030886745$q(electronic bk.)

Standard No.: 10.1007/978-3-030-88674-5doiSubjects--Topical Terms:

797608
Carleman theorem.

LC Class. No.: QA331 / .L4 2022

Dewey Class. No.: 515.9

Elliptic carleman estimates and applications to stabilization and controllability.Volume I,Dirichlet boundary conditions on Euclidean space
LDR:03335nmm a2200349 a 4500 001 623201
003 DE-He213
005 20220328210219.0
006 m d
007 cr nn 008maaau
008 221209s2022 sz s 0 eng d
020 $a 9783030886745$q(electronic bk.)
020 $a 9783030886738$q(paper)
024 7 $a 10.1007/978-3-030-88674-5 $2 doi
035 $a 978-3-030-88674-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331 $b .L4 2022
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.9 $2 23
090 $a QA331 $b .L617 2022
100 1 $a Le Rousseau, Jerome. $3 922613
245 1 0 $a Elliptic carleman estimates and applications to stabilization and controllability. $n Volume I, $p Dirichlet boundary conditions on Euclidean space $h [electronic resource] / $c by Jerome Le Rousseau, Gilles Lebeau, Luc Robbiano.
246 3 0 $a Dirichlet boundary conditions on Euclidean space
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2022.
300 $a viii, 411 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Progress in nonlinear differential equations and their applications, $x 1421-1750 ; $v v. 97
505 0 $a Introduction -- Part 1: Calculus with a Large Parameter, Carleman Estimates Derivation -- (Pseudo-)differential Operators with a Large Parameter -- Carleman Estimate for a Second-Order Elliptic Operator -- Optimality Aspects of Carleman Estimates -- Part 2: Applications of Carleman Estimates -- Unique Continuation -- Stabilization of the Wave Equation with an Inner Damping -- Controllability of Parabolic Equations -- Part 3: Background Material: Analysis and Evolution Equations -- A Short Review of Distribution Theory -- Invariance under Change of Variables -- Elliptic Operator with Dirichlet Data and Associated Semigroup -- Some Elements of Functional Analysis -- Some Elements of Semigroup Theory -- Bibliography -- Subject Index -- Index of Notation.
520 $a 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.
650 0 $a Carleman theorem. $3 797608
650 0 $a Differential equations, Partial. $3 189753
650 1 4 $a Differential Equations. $3 285983
650 2 4 $a Systems Theory, Control. $3 274654
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Functional Analysis. $3 274845
700 1 $a Lebeau, Gilles. $3 467460
700 1 $a Robbiano, Luc. $3 922614
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Progress in nonlinear differential equations and their applications ; $v v.83. $3 558793
856 4 0 $u https://doi.org/10.1007/978-3-030-88674-5
950 $a Mathematics and Statistics (SpringerNature-11649)