Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II : General Boundary Conditions on Riemannian Manifolds

Jérôme Le Rousseau

ISBN 10: 3030886727 / ISBN 13: 9783030886721

Published by Springer International Publishing, 2023

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions.The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.

Seller Inventory # 9783030886721

Bibliographic Details

• Title: Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II : General Boundary Conditions on Riemannian Manifolds
• Publisher: Springer International Publishing
• Publication Date: 2023
• Language: English
• ISBN 10: 3030886727
• ISBN 13: 9783030886721
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 30D millimeters 254 millimeters width by 178 millimeters height by 30 millimeters depth
• Weight: 1040 grams

About this title

Synopsis

This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation.  Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions.

The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds.  Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates.  The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.