Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
Dirichlet Boundary Conditions on Euclidean Space
Series: Progress in Nonlinear Differential Equations and Their Applications; 97;
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Product details:
- Edition number 1st ed. 2022
- Publisher Birkhäuser
- Date of Publication 30 March 2023
- Number of Volumes 1 pieces, Book
- ISBN 9783030886769
- Binding Paperback
- No. of pages411 pages
- Size 254x178 mm
- Weight 795 g
- Language English
- Illustrations 8 Illustrations, black & white; 20 Illustrations, color 499
Categories
Short description:
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.
Long description:
Table of Contents:
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.
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