Product details:
| ISBN13: | 9783030886721 |
| ISBN10: | 3030886727 |
| Binding: | Paperback |
| No. of pages: | 547 pages |
| Size: | 254x178 mm |
| Weight: | 1053 g |
| Language: | English |
| Illustrations: | 8 Illustrations, black & white; 9 Illustrations, color |
| 539 |
Category:
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
General Boundary Conditions on Riemannian Manifolds
Edition number: 1st ed. 2022
Publisher: Birkhäuser
Date of Publication: 23 April 2023
Number of Volumes: 1 pieces, Book
Normal price:
Publisher's listprice:
EUR 181.89
EUR 181.89
Your price:
63 254 (60 242 HUF + 5% VAT )
discount is: 20% (approx 15 813 HUF off)
Discount is valid until: 31 December 2024
The discount is only available for 'Alert of Favourite Topics' newsletter recipients.
Click here to subscribe.
Click here to subscribe.
Availability:
Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
Not in stock at Prospero.
Can't you provide more accurate information?
Not in stock at Prospero.
Short description:
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.
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.
Long description:
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.
Table of Contents:
Introduction.- Part 1: General Boundary Conditions.- Lopatinskii-Sapiro Boundary Conditions.- Fredholm Properties of Second-Order Elliptic Operators.- Selfadjoint Operators under General Boundary Conditions.- Part 2: Carleman Estimates on Riemannian Manifolds.- Estimates on Riemannian Manifolds for Dirichlet Boundary Conditions.- Pseudo-Differential Operators on a Half-Space.- Sobolev Norms with a Large Parameter on a Manifold.- Estimates for General Boundary Conditions.- Part 3: Applications.- Quantified Unique Continuation on a Riemannian Manifold.- Stabilization of Waves under Neumann Boundary Damping.- Spectral Inequality for General Boundary Conditions and Applications.- Part 4: Further Aspects of Carleman Estimates.- Carleman Estimates with Source Terms of Weaker Regularity.- Optimal Estimates at the Boundary.- Background Material: Geometry.- Elements of Differential Geometry.- Integration and Differential Operators on Manifolds.- Elements of Riemannian Geometry.- Sobolev Spacesand Laplace Problems on a Riemannian Manifold.- Bibliography.- Index.- Index of Notation.